该成果属于数理偏微分方程的应用基础研究领域。主要研究了物理、力学及交叉科学中的若干重要非线性偏微分方程的适定性和渐近机制问题，取得了有重要国际影响的研究进展，该成果出版著作1部，发表SCI学术论文四十余篇，包括国际顶尖学...该成果属于数理偏微分方程的应用基础研究领域。主要研究了物理、力学及交叉科学中的若干重要非线性偏微分方程的适定性和渐近机制问题，取得了有重要国际影响的研究进展，该成果出版著作1部，发表SCI学术论文四十余篇，包括国际顶尖学术期刊Adv. Math.（美国）、ARMA、SIAM J M A、CPDE、JDE、M3AS等杂志上。四十余篇论文被美、加、英、法、德、意、日、俄等十余个国家的著名教授、学者SCI广泛引用，并给予高度评价。展开更多
An upwind scheme based on the unstructured mesh is developed to solve ideal 2-D magnetohydrodynamics （MHD） equations. The inviscid fluxes are approximated by using the modified advection upstream splitting method （...An upwind scheme based on the unstructured mesh is developed to solve ideal 2-D magnetohydrodynamics （MHD） equations. The inviscid fluxes are approximated by using the modified advection upstream splitting method （AUSM） scheme, and a 5-stage explicit Runge-Kutta scheme is adopted in the time integration. To avoid the influence of the magnetic field divergence created during the simulation, the hyperbolic divergence cleaning method is introduced. The shock-capturing properties of the method are verified by solving the MHD shock-tube problem. Then the 2-D nozzle flow with the magnetic field is numerically simulated on the unstructured mesh. Computational results demonstrate the effects of the magnetic field and agree well with those from references.展开更多
We investigate initial-boundary-value problem for three-dimensional magnetohydrodynamic （MHD） system of compressible viscous heat-conductive flows and the three-dimensional full compressible Navier-Stokes equations....We investigate initial-boundary-value problem for three-dimensional magnetohydrodynamic （MHD） system of compressible viscous heat-conductive flows and the three-dimensional full compressible Navier-Stokes equations. We establish a blowup criterion only in terms of the derivative of velocity field, similar to the Beale^Kato-Majda type criterion for compressible viscous barotropic flows by Huang et al. （2011）. The results indicate that the nature of the blowup for compressible MHD models of viscous media is similar to the barotropic compressible Navier-Stokes equations and does not depend on further sophistication of the MHD model, in particular, it is independent of the temperature and magnetic field. It also reveals that the deformation tensor of the velocity field plays a more dominant role than the electromagnetic field and the temperature in regularity theory. Especially, the similar results also hold for compressible viscous heat-conductive Navier-Stokes flows, which extend the results established by Fan et al. （2010）, and I-Iuang and Li （2009）. In addition, the viscous coefficients are only restricted by the physical conditions in this paper.展开更多
A theoretical model to explain the mechanism of the electromagnetic wave propagation in the quasi two-dimensional layer of counterions adjacent to the surface of a charged cylindrical membrane is presented. By using M...A theoretical model to explain the mechanism of the electromagnetic wave propagation in the quasi two-dimensional layer of counterions adjacent to the surface of a charged cylindrical membrane is presented. By using Maxwell and hydrodynamic equations with appropriate boundary conditions, general expression of dispersion relation is obtained for the electromagnetic wave with mixed TE and TM modes.展开更多
文摘该成果属于数理偏微分方程的应用基础研究领域。主要研究了物理、力学及交叉科学中的若干重要非线性偏微分方程的适定性和渐近机制问题，取得了有重要国际影响的研究进展，该成果出版著作1部，发表SCI学术论文四十余篇，包括国际顶尖学术期刊Adv. Math.（美国）、ARMA、SIAM J M A、CPDE、JDE、M3AS等杂志上。四十余篇论文被美、加、英、法、德、意、日、俄等十余个国家的著名教授、学者SCI广泛引用，并给予高度评价。
文摘An upwind scheme based on the unstructured mesh is developed to solve ideal 2-D magnetohydrodynamics （MHD） equations. The inviscid fluxes are approximated by using the modified advection upstream splitting method （AUSM） scheme, and a 5-stage explicit Runge-Kutta scheme is adopted in the time integration. To avoid the influence of the magnetic field divergence created during the simulation, the hyperbolic divergence cleaning method is introduced. The shock-capturing properties of the method are verified by solving the MHD shock-tube problem. Then the 2-D nozzle flow with the magnetic field is numerically simulated on the unstructured mesh. Computational results demonstrate the effects of the magnetic field and agree well with those from references.
基金supported by National Natural Science Foundation of China(Grant Nos.11171236 and 71372189)Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT1273)+1 种基金Sichuan Youth Science and Technology Foundation(Grant No.2014JQ0003)China Postdoctoral Science Foundation(Grant No.2013M542285)
文摘We investigate initial-boundary-value problem for three-dimensional magnetohydrodynamic （MHD） system of compressible viscous heat-conductive flows and the three-dimensional full compressible Navier-Stokes equations. We establish a blowup criterion only in terms of the derivative of velocity field, similar to the Beale^Kato-Majda type criterion for compressible viscous barotropic flows by Huang et al. （2011）. The results indicate that the nature of the blowup for compressible MHD models of viscous media is similar to the barotropic compressible Navier-Stokes equations and does not depend on further sophistication of the MHD model, in particular, it is independent of the temperature and magnetic field. It also reveals that the deformation tensor of the velocity field plays a more dominant role than the electromagnetic field and the temperature in regularity theory. Especially, the similar results also hold for compressible viscous heat-conductive Navier-Stokes flows, which extend the results established by Fan et al. （2010）, and I-Iuang and Li （2009）. In addition, the viscous coefficients are only restricted by the physical conditions in this paper.
文摘A theoretical model to explain the mechanism of the electromagnetic wave propagation in the quasi two-dimensional layer of counterions adjacent to the surface of a charged cylindrical membrane is presented. By using Maxwell and hydrodynamic equations with appropriate boundary conditions, general expression of dispersion relation is obtained for the electromagnetic wave with mixed TE and TM modes.
