We investigate the asymptotic behavior of solutions to the initial boundary value problem for the micropolar fluid model in a half line R+:=(0,∞).Inspired by the relationship between a micropolar fluid model and Navi...We investigate the asymptotic behavior of solutions to the initial boundary value problem for the micropolar fluid model in a half line R+:=(0,∞).Inspired by the relationship between a micropolar fluid model and Navier-Stokes equations,we prove that the composite wave consisting of the transonic boundary layer solution,the 1-rarefaction wave,the viscous 2-contact wave and the 3-rarefaction wave for the inflow problem on the micropolar fluid model is time-asymptotic ally stable under some smallness conditions.Meanwhile,we obtain the global existence of solutions based on the basic energy method.展开更多
Chiral methyl mandelates are useful synthons in organic transformation and pharmaceutical synthesis.Green synthesis of these valuable compounds by direct C–H activating oxidative hydroxylation has attracted keen inte...Chiral methyl mandelates are useful synthons in organic transformation and pharmaceutical synthesis.Green synthesis of these valuable compounds by direct C–H activating oxidative hydroxylation has attracted keen interest.Described herein is achieving the stereoselective and efficient bio-hydroxylation of methyl 2-phenylacetates to the chiral methyl mandelates by directed evolution of the cytochrome P450DA hydroxylase.In the present study,a new colorimetric high-throughput screening assay was successfully developed based on a dualenzyme cascade for the engineering of the P450DA's hydroxylation activity.Several beneficial variants with enhanced bio-hydroxylation activity were created by combining random mutagenesis and site-saturated/directed mutagenesis strategies.Whole-cell bio-hydroxylation of various methyl 2-phenylacetates using the best septupletmutant P450DA-11 yielded the corresponding chiral methyl mandelates in up to 92%isolated yields and>99%ee.展开更多
This paper is concerned with the asymptotic behavior of the solution to the Euler equations with time-depending damping on quadrant(x,t)∈R^+×R^+,with the null-Dirichlet boundary condition or the null-Neumann bou...This paper is concerned with the asymptotic behavior of the solution to the Euler equations with time-depending damping on quadrant(x,t)∈R^+×R^+,with the null-Dirichlet boundary condition or the null-Neumann boundary condition on u. We show that the corresponding initial-boundary value problem admits a unique global smooth solution which tends timeasymptotically to the nonlinear diffusion wave. Compared with the previous work about Euler equations with constant coefficient damping, studied by Nishihara and Yang(1999), and Jiang and Zhu(2009, Discrete Contin Dyn Syst), we obtain a general result when the initial perturbation belongs to the same space. In addition,our main novelty lies in the fact that the cut-off points of the convergence rates are different from our previous result about the Cauchy problem. Our proof is based on the classical energy method and the analyses of the nonlinear diffusion wave.展开更多
基金The research was supported by the National Natural Science Foundation of China(11601164,11971183)the Fundamental Research Funds for the Central Universities(ZQN-701)the Natural Science Foundation of Fujian Province of China(2020J01071).
文摘We investigate the asymptotic behavior of solutions to the initial boundary value problem for the micropolar fluid model in a half line R+:=(0,∞).Inspired by the relationship between a micropolar fluid model and Navier-Stokes equations,we prove that the composite wave consisting of the transonic boundary layer solution,the 1-rarefaction wave,the viscous 2-contact wave and the 3-rarefaction wave for the inflow problem on the micropolar fluid model is time-asymptotic ally stable under some smallness conditions.Meanwhile,we obtain the global existence of solutions based on the basic energy method.
基金supported by the National Natural Science Foundation of China(Nos.21961048 and 32271537)Science and Technology Department of Zunyi(Nos.ZSKRPT-2020-5,ZSKH-2018-3 and ZSKRPT-2021-5).
文摘Chiral methyl mandelates are useful synthons in organic transformation and pharmaceutical synthesis.Green synthesis of these valuable compounds by direct C–H activating oxidative hydroxylation has attracted keen interest.Described herein is achieving the stereoselective and efficient bio-hydroxylation of methyl 2-phenylacetates to the chiral methyl mandelates by directed evolution of the cytochrome P450DA hydroxylase.In the present study,a new colorimetric high-throughput screening assay was successfully developed based on a dualenzyme cascade for the engineering of the P450DA's hydroxylation activity.Several beneficial variants with enhanced bio-hydroxylation activity were created by combining random mutagenesis and site-saturated/directed mutagenesis strategies.Whole-cell bio-hydroxylation of various methyl 2-phenylacetates using the best septupletmutant P450DA-11 yielded the corresponding chiral methyl mandelates in up to 92%isolated yields and>99%ee.
基金supported by National Natural Science Foundation of China (Grant Nos. 11331005,11771150,11601164 and 11601165)
文摘This paper is concerned with the asymptotic behavior of the solution to the Euler equations with time-depending damping on quadrant(x,t)∈R^+×R^+,with the null-Dirichlet boundary condition or the null-Neumann boundary condition on u. We show that the corresponding initial-boundary value problem admits a unique global smooth solution which tends timeasymptotically to the nonlinear diffusion wave. Compared with the previous work about Euler equations with constant coefficient damping, studied by Nishihara and Yang(1999), and Jiang and Zhu(2009, Discrete Contin Dyn Syst), we obtain a general result when the initial perturbation belongs to the same space. In addition,our main novelty lies in the fact that the cut-off points of the convergence rates are different from our previous result about the Cauchy problem. Our proof is based on the classical energy method and the analyses of the nonlinear diffusion wave.
