In this paper,we study the Radon measure initial value problem for the nonisentropic improved Aw-Rascle-Zhang model.For arbitrary convex F(u)in this model we construct the Riemann solutions by elementary waves andδ-s...In this paper,we study the Radon measure initial value problem for the nonisentropic improved Aw-Rascle-Zhang model.For arbitrary convex F(u)in this model we construct the Riemann solutions by elementary waves andδ-shock waves using the method of generalized characteristic analysis.We obtain the solutions constructively for initial data containing the Dirac measure by taking the limit of the solutions for that with three piecewise constants.Moreover,we analyze different kinds of wave interactions,including the interactions of theδ-shock waves with elementary waves.展开更多
The motion of the self-gravitational gaseous stars can be described by the Euler-Poisson equations. The main purpose of this paper is concerned with the existence of stationary solutions of Euler-Poisson equations for...The motion of the self-gravitational gaseous stars can be described by the Euler-Poisson equations. The main purpose of this paper is concerned with the existence of stationary solutions of Euler-Poisson equations for some velocity fields and entropy functions that solve the conservation of mass and energy. Under different restriction to the strength of velocity field, we get the existence and multiplicity of the stationary solutions of Euler-Poisson system.展开更多
In this paper, we study the vanishing viscosity limit for non-isentropic gas dy- namics with interacting shocks. Given any entropy solution of non-isentropic gas dynamics which consists of two different families of sh...In this paper, we study the vanishing viscosity limit for non-isentropic gas dy- namics with interacting shocks. Given any entropy solution of non-isentropic gas dynamics which consists of two different families of shocks interacting at some positive time, we show that such solution is the vanishing viscosity limit of a family of smooth global solutions for a viscous system of conservation law. We remark that, after the interacting time, not only shocks but also contact discontinuity are generated.展开更多
The motion of the self-gravitational gaseous stars can be described by the Euler-Poisson equations. The main purpose of this article is concerned with the nonlinear stability of gaseous stars in the non-isentropic cas...The motion of the self-gravitational gaseous stars can be described by the Euler-Poisson equations. The main purpose of this article is concerned with the nonlinear stability of gaseous stars in the non-isentropic case, when 34 γ2, S（x,t） is a smooth bounded function. First, we verify that the steady states are minimizers of the energy via concentration-compactness method; then using the variational approach we obtain the stability results of the non-isentropic flow.展开更多
The incompressible limit of the non-isentropic magnetohydrodynamic equations with zero thermal coefficient, in a two dimensional bounded domain with the Dirichlet condi- tion for velocity and perfectly conducting boun...The incompressible limit of the non-isentropic magnetohydrodynamic equations with zero thermal coefficient, in a two dimensional bounded domain with the Dirichlet condi- tion for velocity and perfectly conducting boundary condition for magnetic field, is rigorously justified.展开更多
The compressible non-isentropic bipolar Navier-Stokes-Poisson （BNSP） sys- tem is investigated in R3 in the present paper, and the optimal time decay rates of global strong solution are shown. For initial data being ...The compressible non-isentropic bipolar Navier-Stokes-Poisson （BNSP） sys- tem is investigated in R3 in the present paper, and the optimal time decay rates of global strong solution are shown. For initial data being a perturbation of equilibrium state in Hl（R3） （R3） for 1 〉 4 and s E （0, 1], it is shown that the density and temperature for each charged particle （like electron or ion） decay at the same optimal rate （1 ＋ t）-3/4, but the momentum for each particle decays at the optimal rate （1 ＋ t）-1/4-3/2 which is slower than the rate （1 ＋ t）-3/4-3/2 for the compressible Navier-Stokes （NS） equations [19] for same initial data. However, the total momentum tends to the constant state at the rate （1 ＋t）-3/4 as well, due to the interplay interaction of charge particles which counteracts the influence of electric field.展开更多
We consider a non-isentropic Euler-Poisson system with two small parameters arising in the modeling of unmagnetized plasmas and semiconductors.On the basis of the energy estimates and the compactness theorem,the unifo...We consider a non-isentropic Euler-Poisson system with two small parameters arising in the modeling of unmagnetized plasmas and semiconductors.On the basis of the energy estimates and the compactness theorem,the uniform global existence of the solutions and the combined quasi-neutral and zero-electron-mass limit of the system are proved when the initial data are close to the constant equilibrium state.In particular,the limit is rigorously justified as the two parameters tend to zero independently.展开更多
In this paper, we study the non-isentropic compressible magnetohydrodynamic system with a time periodic external force in R^n. Under the condition that the optimal time decay rates are obtained by spectral analysis, w...In this paper, we study the non-isentropic compressible magnetohydrodynamic system with a time periodic external force in R^n. Under the condition that the optimal time decay rates are obtained by spectral analysis, we show that the existence, uniqueness and time-asymptotic stability of time periodic solutions when the space dimension n 〉 5. Our proof is based on a combination of the energy method and the contraction mapping theorem.展开更多
This paper verifies the low Mach number limit of the non-isentropic compressible magnetohydrodynamic(MHD)equations with or without the magnetic diffusion in a three-dimensional bounded domain when the temperature vari...This paper verifies the low Mach number limit of the non-isentropic compressible magnetohydrodynamic(MHD)equations with or without the magnetic diffusion in a three-dimensional bounded domain when the temperature variation is large but finite.The uniform estimates of strong solutions are established in a short time interval independent of the Mach number,provided that the slip boundary condition for the velocity and the Neumann boundary condition for the temperature are imposed and the initial data is well-prepared.展开更多
We investigate the zero dielectric constant limit to the non-isentropic compressible Euler-Maxwell system.We justify this singular limit rigorously in the framework of smooth solutions and obtain the nonisentropic com...We investigate the zero dielectric constant limit to the non-isentropic compressible Euler-Maxwell system.We justify this singular limit rigorously in the framework of smooth solutions and obtain the nonisentropic compressible magnetohydrodynamic equations as the dielectric constant tends to zero.展开更多
The authors investigate the global existence and asymptotic behavior of classical solutions to the 3D non-isentropic compressible Euler equations with damping on a bounded domain with slip boundary condition. The glob...The authors investigate the global existence and asymptotic behavior of classical solutions to the 3D non-isentropic compressible Euler equations with damping on a bounded domain with slip boundary condition. The global existence and uniqueness of classical solutions are obtained when the initial data are near an equilibrium. Furthermore,the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.展开更多
This paper is contributed to the structural stability of multi-wave configurations to Cauchy problem for the compressible non-isentropic Euler system with adiabatic exponentγ∈(1,3].Given some small BV perturbations ...This paper is contributed to the structural stability of multi-wave configurations to Cauchy problem for the compressible non-isentropic Euler system with adiabatic exponentγ∈(1,3].Given some small BV perturbations of the initial state,the author employs a modified wave front tracking method,constructs a new Glimm functional,and proves its monotone decreasing based on the possible local wave interaction estimates,then establishes the global stability of the multi-wave configurations,consisting of a strong 1-shock wave,a strong 2-contact discontinuity,and a strong 3-shock wave,without restrictions on their strengths.展开更多
This paper proves the existence of variational rotating solutions to the compressible non-isentropic Euler-Poisson equations with prescribed total mass.This extends the result of the isentropic case(see Auchmuty and B...This paper proves the existence of variational rotating solutions to the compressible non-isentropic Euler-Poisson equations with prescribed total mass.This extends the result of the isentropic case(see Auchmuty and Beals(1971))to the non-isentropic case.Compared with the previous result of variational rotating solutions in the non-isentropic case(see Wu(2015)),to keep the constraint of prescribed finite total mass,we establish a new variational structure of the non-isentropic Euler-Poisson equations.展开更多
Abstract The bipolar non-isentropic compressible Navier-Stokes-Poisson （BNSP） system is investigated in R3 in the present paper, and the optimal L2 time decay rate for the global classical solution is established. I...Abstract The bipolar non-isentropic compressible Navier-Stokes-Poisson （BNSP） system is investigated in R3 in the present paper, and the optimal L2 time decay rate for the global classical solution is established. It is shown that the total densities, total momenta and total temperatures of two carriers converge to the equilibrium states at the rate （1 ＋ t）-3/4＋εin L2-norm for any small and fix ε 〉 0. But, both the difference of densities and the difference of temperatures of two carriers decay at the optimal rate （1 ＋ t）- 3/4, and the difference of momenta decays at the optimal rate （1 ＋t）- 1/4. This phenomenon on the charge transport shows the essential difference between the non-isentropic unipolar NSP and the bipolar NSP system.展开更多
We study in this article the compressible heat-conducting Navier-Stokes equations in periodic domain driven by a time-periodic external force. The existence of the strong time-periodic solution is established by a new...We study in this article the compressible heat-conducting Navier-Stokes equations in periodic domain driven by a time-periodic external force. The existence of the strong time-periodic solution is established by a new approach. First, we reformulate the system and consider some decay estimates of the linearized system.Under some smallness and symmetry assumptions on the external force, the existence of the time-periodic solution of the linearized system is then identi?ed as the ?xed point of a Poincare′ map which is obtained by the Tychonoff ?xed point theorem.Although the Tychonoff ?xed point theorem cannot directly ensure the uniqueness,but we could construct a set-valued function, the ?xed point of which is the timeperiodic solution of the original system. At last, the existence of the ?xed point is obtained by the Kakutani ?xed point theorem. In addition, the uniqueness of timeperiodic solution is also studied.展开更多
In this article,by the mean-integral of the conserved quantity,we prove that the one-dimensional non-isentropic gas dynamic equations in an ideal gas state do not possess a bounded invariant region.Moreover,we obtain ...In this article,by the mean-integral of the conserved quantity,we prove that the one-dimensional non-isentropic gas dynamic equations in an ideal gas state do not possess a bounded invariant region.Moreover,we obtain a necessary condition on the state equations for the existence of an invariant region for a non-isentropic process.Finally,we provide a mat hematical example showing that with a special state equation,a bounded invariant region for the non-isentropic process may exist.展开更多
The quasi-neutral limit of the multi-dimensional non-isentropic bipolar Euler-Poisson system is considered in the present paper. It is shown that for well-prepared initial data the smooth solution of the non-isentropi...The quasi-neutral limit of the multi-dimensional non-isentropic bipolar Euler-Poisson system is considered in the present paper. It is shown that for well-prepared initial data the smooth solution of the non-isentropic bipolar Euler-Poisson system converges strongly to the compressible non-isentropic Euler equations as the Debye length goes to zero.展开更多
基金supported by the Natural Science Foundation of Zhejiang(LQ18A010004)Matematical Analysis,The First class courses in Zhejiang Province(210052)+1 种基金the Fundamental Research Funds for the Provincial Universities of Zhejiang(210039)supported by the National Natural Science Foundation of China(11771442)。
文摘In this paper,we study the Radon measure initial value problem for the nonisentropic improved Aw-Rascle-Zhang model.For arbitrary convex F(u)in this model we construct the Riemann solutions by elementary waves andδ-shock waves using the method of generalized characteristic analysis.We obtain the solutions constructively for initial data containing the Dirac measure by taking the limit of the solutions for that with three piecewise constants.Moreover,we analyze different kinds of wave interactions,including the interactions of theδ-shock waves with elementary waves.
基金supported by NSFC (10631030, 11071094)the fund of CCNU for Ph.D students (2009021)
文摘The motion of the self-gravitational gaseous stars can be described by the Euler-Poisson equations. The main purpose of this paper is concerned with the existence of stationary solutions of Euler-Poisson equations for some velocity fields and entropy functions that solve the conservation of mass and energy. Under different restriction to the strength of velocity field, we get the existence and multiplicity of the stationary solutions of Euler-Poisson system.
基金Xiaoding Shi was supported by National Natural Sciences Foundation of China(11471321)Yan Yong was supported by National Natural Sciences Foundation of China(11201301)
文摘In this paper, we study the vanishing viscosity limit for non-isentropic gas dy- namics with interacting shocks. Given any entropy solution of non-isentropic gas dynamics which consists of two different families of shocks interacting at some positive time, we show that such solution is the vanishing viscosity limit of a family of smooth global solutions for a viscous system of conservation law. We remark that, after the interacting time, not only shocks but also contact discontinuity are generated.
基金supported by NSFC (10631030)the fund of CCNU for Ph.D Students (2009021)
文摘The motion of the self-gravitational gaseous stars can be described by the Euler-Poisson equations. The main purpose of this article is concerned with the nonlinear stability of gaseous stars in the non-isentropic case, when 34 γ2, S（x,t） is a smooth bounded function. First, we verify that the steady states are minimizers of the energy via concentration-compactness method; then using the variational approach we obtain the stability results of the non-isentropic flow.
基金supported by NSFC(11371042)China 973 program(2011 CB808002)+2 种基金BSFC(1132006)CIT&TCD(20130312)the fund of the Beijing Education Committee(KZ 201210005005)
文摘The incompressible limit of the non-isentropic magnetohydrodynamic equations with zero thermal coefficient, in a two dimensional bounded domain with the Dirichlet condi- tion for velocity and perfectly conducting boundary condition for magnetic field, is rigorously justified.
基金supported by the NSFC (10871134)supported by the NSFC (10871134,10910401059)+1 种基金the funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (PHR201006107)supported by the General Research Fund of Hong Kong,City Univ.103108
文摘The compressible non-isentropic bipolar Navier-Stokes-Poisson （BNSP） sys- tem is investigated in R3 in the present paper, and the optimal time decay rates of global strong solution are shown. For initial data being a perturbation of equilibrium state in Hl（R3） （R3） for 1 〉 4 and s E （0, 1], it is shown that the density and temperature for each charged particle （like electron or ion） decay at the same optimal rate （1 ＋ t）-3/4, but the momentum for each particle decays at the optimal rate （1 ＋ t）-1/4-3/2 which is slower than the rate （1 ＋ t）-3/4-3/2 for the compressible Navier-Stokes （NS） equations [19] for same initial data. However, the total momentum tends to the constant state at the rate （1 ＋t）-3/4 as well, due to the interplay interaction of charge particles which counteracts the influence of electric field.
基金partially supported by the ISFNSFC joint research program(11761141008)NSFC(12071044 and 12131007)the NSF of Jiangsu Province(BK20191296)。
文摘We consider a non-isentropic Euler-Poisson system with two small parameters arising in the modeling of unmagnetized plasmas and semiconductors.On the basis of the energy estimates and the compactness theorem,the uniform global existence of the solutions and the combined quasi-neutral and zero-electron-mass limit of the system are proved when the initial data are close to the constant equilibrium state.In particular,the limit is rigorously justified as the two parameters tend to zero independently.
基金Supported by National Natural Science Foundation of China(11271305)
文摘In this paper, we study the non-isentropic compressible magnetohydrodynamic system with a time periodic external force in R^n. Under the condition that the optimal time decay rates are obtained by spectral analysis, we show that the existence, uniqueness and time-asymptotic stability of time periodic solutions when the space dimension n 〉 5. Our proof is based on a combination of the energy method and the contraction mapping theorem.
基金supported by National Natural Science Foundation of China(Grant Nos.11971477,12131007 and 11761141008)the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(Grant No.18XNLG30)。
文摘This paper verifies the low Mach number limit of the non-isentropic compressible magnetohydrodynamic(MHD)equations with or without the magnetic diffusion in a three-dimensional bounded domain when the temperature variation is large but finite.The uniform estimates of strong solutions are established in a short time interval independent of the Mach number,provided that the slip boundary condition for the velocity and the Neumann boundary condition for the temperature are imposed and the initial data is well-prepared.
基金supported by National Basic Research Program of China (Grant No. 2011CB309705)National Natural Science Foundation of China (Grant Nos. 11229101, 11371065 and 11271184)+2 种基金Program for New Century Excellent Talents in University (Grant No. 110227)the Priority Academic Program Development of Jiangsu Higher Education Institutionsthe Fundamental Research Funds for the Central Universities
文摘We investigate the zero dielectric constant limit to the non-isentropic compressible Euler-Maxwell system.We justify this singular limit rigorously in the framework of smooth solutions and obtain the nonisentropic compressible magnetohydrodynamic equations as the dielectric constant tends to zero.
基金supported by the National Natural Science Foundation of China(Nos.11301172,11226170,11571280)the Scientific Research Fund of Hunan Provincial Education Department(No.14B077)
文摘The authors investigate the global existence and asymptotic behavior of classical solutions to the 3D non-isentropic compressible Euler equations with damping on a bounded domain with slip boundary condition. The global existence and uniqueness of classical solutions are obtained when the initial data are near an equilibrium. Furthermore,the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.
基金supported by the National Natural Science Foundation of China(No.11701435)the Fundamental Research Funds for the Central Universities(WUT:2020IB018)。
文摘This paper is contributed to the structural stability of multi-wave configurations to Cauchy problem for the compressible non-isentropic Euler system with adiabatic exponentγ∈(1,3].Given some small BV perturbations of the initial state,the author employs a modified wave front tracking method,constructs a new Glimm functional,and proves its monotone decreasing based on the possible local wave interaction estimates,then establishes the global stability of the multi-wave configurations,consisting of a strong 1-shock wave,a strong 2-contact discontinuity,and a strong 3-shock wave,without restrictions on their strengths.
基金supported by National Natural Science Foundation of China(Grant Nos.11901208 and 11971009)。
文摘This paper proves the existence of variational rotating solutions to the compressible non-isentropic Euler-Poisson equations with prescribed total mass.This extends the result of the isentropic case(see Auchmuty and Beals(1971))to the non-isentropic case.Compared with the previous result of variational rotating solutions in the non-isentropic case(see Wu(2015)),to keep the constraint of prescribed finite total mass,we establish a new variational structure of the non-isentropic Euler-Poisson equations.
基金Supported by the National Natural Science Foundation of China(No.10872004)
文摘Abstract The bipolar non-isentropic compressible Navier-Stokes-Poisson （BNSP） system is investigated in R3 in the present paper, and the optimal L2 time decay rate for the global classical solution is established. It is shown that the total densities, total momenta and total temperatures of two carriers converge to the equilibrium states at the rate （1 ＋ t）-3/4＋εin L2-norm for any small and fix ε 〉 0. But, both the difference of densities and the difference of temperatures of two carriers decay at the optimal rate （1 ＋ t）- 3/4, and the difference of momenta decays at the optimal rate （1 ＋t）- 1/4. This phenomenon on the charge transport shows the essential difference between the non-isentropic unipolar NSP and the bipolar NSP system.
基金The NSF(20170520047JH) for Young Scientists of Jilin Provincethe Scientific and Technological Project(JJKH20190180KJ) of Jilin Province’s Education Department in Thirteenth Five-Year
文摘We study in this article the compressible heat-conducting Navier-Stokes equations in periodic domain driven by a time-periodic external force. The existence of the strong time-periodic solution is established by a new approach. First, we reformulate the system and consider some decay estimates of the linearized system.Under some smallness and symmetry assumptions on the external force, the existence of the time-periodic solution of the linearized system is then identi?ed as the ?xed point of a Poincare′ map which is obtained by the Tychonoff ?xed point theorem.Although the Tychonoff ?xed point theorem cannot directly ensure the uniqueness,but we could construct a set-valued function, the ?xed point of which is the timeperiodic solution of the original system. At last, the existence of the ?xed point is obtained by the Kakutani ?xed point theorem. In addition, the uniqueness of timeperiodic solution is also studied.
基金supported by the Natural Science Foundation of Zhejiang(LQ18A010004)the second author was supported by the Fundamental Research Funds for the Central Universities(WUT:2020IB011).
文摘In this article,by the mean-integral of the conserved quantity,we prove that the one-dimensional non-isentropic gas dynamic equations in an ideal gas state do not possess a bounded invariant region.Moreover,we obtain a necessary condition on the state equations for the existence of an invariant region for a non-isentropic process.Finally,we provide a mat hematical example showing that with a special state equation,a bounded invariant region for the non-isentropic process may exist.
基金supported by National Natural Science Foundation of China(Grant No.40890154)National Basic Research Program(Grant No.2005CB321700)+5 种基金supported by National Natural Science Foundation of China(Grant No.10701011)supported by National Natural Science Foundation of China(Grant No.10431060)Beijing Nova Program,Program for New Century Excellent Talentsin University,Huo Ying Dong Foundation(Grant No.111033)supported by National Natural Science Foundation of China(Grant No.10901011)Beijing Municipal Natural Science Foundation(Grant No.1102009)Foundation for Talents of Beijing(Grant No.20081D0501500171)
文摘The quasi-neutral limit of the multi-dimensional non-isentropic bipolar Euler-Poisson system is considered in the present paper. It is shown that for well-prepared initial data the smooth solution of the non-isentropic bipolar Euler-Poisson system converges strongly to the compressible non-isentropic Euler equations as the Debye length goes to zero.
