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Chinese Annals of Mathematics,Series B 2008年第4期29卷 441-458页

作者： Junping YIN Zhong TAN Department of Mathematics Xiamen University Xiamen 361005 Fujian China.

The authors prove two global existence results of strong solutions of the isentropic compressible navier-stokes-poisson equations in one-dimensional bounded intervals. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition. In this paper the initial vacuum is allowed, and T is bounded.

关键词： Global strong solutions navier-stokes-poisson equations Existence and uniqueness

Stability of Weak Solutions for the Compressible navier-stokes-poisson equations

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Acta Mathematicae Applicatae Sinica 2012年第3期28卷 597-606页

作者： Ru-xu LIAN Ming-jie LI College of Mathematics and Information Science North China University of Water Resources and Electric PowerZhengzhou 450011China School of Mathematical Sciences Capital Normal UniversityBeijing 100048China

In this paper, we consider the isentropic compressible navier-stokes-poisson equations arising from transport of charged particles or motion of gaseous stars in astrophysics. We are interested in the case that the viscosity coefficients depend on the density and shall degenerate in the appearance of （density） vacuum, and show the Ll-stability of weak solutions for arbitrarily large data on spatial multi-dimensional bounded or periodic domain or whole space.

关键词： compressible fluid navier-stokes-poisson equations stability

Singular limits for the navier-stokes-poisson equations of the viscous plasma with the strong density boundary layer

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Science China Mathematics 2023年第7期66卷 1495-1528页

作者： Qiangchang Ju Tao Luo Xin Xu Institute of Applied Physics and Computational Mathematics Beijing 100088China Department of Mathematics City University of Hong KongHong KongChina School of Mathematical Sciences and College of Oceanic and Atmospheric Sciences Ocean University of ChinaQingdao 266100China

The quasi-neutral limit of the navier-stokes-poisson system modeling a viscous plasma with vanishing viscosity coefficients in the half-space■is rigorously proved under a navier-slip boundary condition for velocity and the Dirichlet boundary condition for electric *** is achieved by establishing the nonlinear stability of the approximation solutions involving the strong boundary layer in density and electric potential,which comes from the breakdown of the quasi-neutrality near the boundary,and dealing with the difficulty of the interaction of this strong boundary layer with the weak boundary layer of the velocity field.

关键词： navier-stokes-poisson equations interaction of strong and weak boundary layers singular limit

STRONG SOLUTIONS OF THE COUPLED navier-stokes-poisson equations FOR ISENTROPIC COMPRESSIBLE FLUIDS

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Acta Mathematica Scientia 2010年第4期30卷 1280-1290页

作者：谭忠张映辉 School of Mathematical Sciences Xiamen University Department of Mathematics Hunan Institute of Science and Technology

In this article, we are concerned with the strong solutions of the coupled navier-stokes-poisson equations for isentropic compressible fluids in a domain Ω R^3. We prove the local existence of unique strong solutions provided that the initial data u0 and u0 satisfy a nature compatibility condition. The important point in this article is that we allow the initial vacuum： the initial density may vanish in an open subset of Ω. This is achieved by getting some uniform estimates and using a Schauder fixed point theorem.

关键词： Strong solutions navier-stokes-poisson equations Schauder fixed point theorem

Global Existence of the Radially Symmetric Strong Solution to navier-stokes-poisson equations for Isentropic Compressible Fluids

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Acta Mathematica Sinica,English Series 2009年第10期25卷 1703-1720页

作者： Jun Ping YIN Zhong TAN Department of Mathematics Xiamen University Xiamen 361005 P. R. China

We prove the two existence results of the radially symmetric strong solutions to the navier- stokes-poisson equations for isentropic compressible fluids. The important point in this paper is that the initial density i... 详细信息

关键词： navier-stokes-poisson equations annular domain radially symmetric solution strong solution existence

Propagation of Density-Oscillations in Solutions to the Compressible navier-stokes-poisson System

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Chinese Annals of Mathematics,Series B 2008年第5期29卷 501-520页

作者： Zhong TAN Yanjin WANG Department of Mathematics Xiamen University Xiamen 361005 Fujian China Department of Mathematics Xiamen UniversityXiamen 3610051 Fujian China

Concerning a bounded sequence of finite energy weak solutions to the compressible navier-stokes-poisson system (denoted by CNSP), which converges up to extraction of a subsequence, the limit system may not be the same system. By introducing Young measures as in [6, 15], the authors deduce the system (HCNSP) which the limit functions must satisfy. Then they solve this system in a subclass where Young measures are convex combinations of Dirac measures, to give the information on the propagation of density-oscillations. The results for strong solutions to (CNSP) (see Corollary 6.1) are also obtained.

关键词： Compressible fluids navier-stokes-poisson equations Young measures Propagation of oscillations Strong solutions