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ASYMPTOTIC BEHAVIOR OF global smooth solutions FOR BIPOLAR COMPRESSIBLE NAVIER-STOKES-MAXWELL SYSTEM FROM PLASMAS

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Acta Mathematica Scientia 2015年第5期35卷 955-969页

作者：冯跃红王术李新 College of Applied Sciences Beijing University of Technology Laboratoire de Mathématiques Université Blaise Pascal Department of Mathematics and Computer Science Xinyang Vocational and Technical College

This paper is concerned with the bipolar compressible Navier-Stokes-Maxwell system for plasmas. We investigated, by means of the techniques of symmetrizer and elaborate energy method, the Cauchy problem in R^3. Under the assumption that the initial values are close to a equilibrium solutions, we prove that the smooth solutions of this problem converge to a steady state as the time goes to the infinity. It is shown that the difference of densities of two carriers converge to the equilibrium states with the norm ｜｜·｜｜H^s-1, while the velocities and the electromagnetic fields converge to the equilibrium states with weaker norms than ｜｜·｜｜H^s-1. This phenomenon on the charge transport shows the essential difference between the unipolar Navier-Stokes-Maxwell and the bipolar Navier-Stokes-Maxwell system.

关键词： bipolar compressible Navier-Stokes-Maxwell system plasmas global smooth solutions energy estimates large-time behavior

solutions to Some Open Problems in Fluid Dynamics

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Chinese Annals of Mathematics,Series B 2008年第2期29卷 179-198页

作者： Linghai ZHANG Department of Mathematics Lehigh University 14 East Packer Avenue Bethlehem Pennsylvania 18015

Let u=u（x,t,uo）represent the global solution of the initial value problem for the one-dimensional fluid dynamics equation ut-εuxxt＋δux＋γHuxx＋βuxxx＋f（u）x=αuxx,u（x,0）=uo（x）, whereα〉0,β〉0,γ〉0,δ〉0 andε〉0 are *** equation may be viewed as a one-dimensional reduction of n-dimensional incompressible Navier-Stokes equations. The nonlinear function satisfies the conditions f（0）=0,｜f（u）｜→∞as ｜u｜→∞,and f∈C^1（R）,and there exist the following limits Lo=lim sup/u→o f（u）/u^3 and L∞=lim sup/u→∞ f（u）/u^5 Suppose that the initial function u0∈L^I（R）∩H^2（R）.By using energy estimates,Fourier transform,Plancherel＇s identity,upper limit estimate,lower limit estimate and the results of the linear problem vt-εv（xxt）＋δvx＋γHv（xx）＋βv（xxx）=αv（xx）,v（x,0）=vo（x）, the author justifies the following limits（with sharp rates of decay） lim t→∞[（1＋t）^（m＋1/2）∫｜uxm（x,t）｜^2dx]=1/2π（π/2α）^（1/2）m!!/（4α）^m[∫R uo（x）dx]^2, if∫R uo（x）dx≠0, where 0!!=1,1!!=1 and m!!=1·3…（2m-3）…（2m-1）.Moreover lim t→∞[（1＋t）^（m＋3/2）∫R｜uxm（x,t）｜^2dx]=1/2π（x/2α）^（1/2）（m＋1）!!/（4α）^（m＋1）[∫Rρo（x）dx]^2, if the initial function uo（x）=ρo′（x）,for some functionρo∈C^1（R）∩L^1（R）and∫Rρo（x）dx≠0.

关键词： Exact limits Sharp rates of decay Fluid dynamics equation global smooth solutions

THE global COMBINED QUASI-NEUTRAL AND ZERO-ELECTRON-MASS LIMIT OF NON-ISENTROPIC EULER-POISSON SYSTEMS

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Acta Mathematica Scientia 2022年第4期42卷 1666-1680页

作者： Yongfu YANG Qiangchang JU Shuang ZHOU College of Science Hohai UniversityNanjing 211100China Institute of Applied Physics and Computational Mathematics Beijing 100088 China Chengxi Junior High School Suzhou215128 China

We consider a non-isentropic Euler-Poisson system with two small parameters arising in the modeling of unmagnetized plasmas and *** 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 *** particular,the limit is rigorously justified as the two parameters tend to zero independently.

关键词： Non-isentropic Euler-Poisson system global smooth solutions uniform energy estimates global convergence compactness

Asymptotic Behavior of the solutions to the One-Dimensional Nonisentropic Hydrodynamic Model for Semiconductors

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Wuhan University Journal of Natural Sciences 2008年第2期13卷 141-147页

作者： LI Yeping Department of Mathematics Shanghai Normal UniversityShanghai 200234 China

In this paper, the asymptotic behavior of the global smooth solutions to the Cauchy problem for the one-dimensional nonisentropic Euler-Poisson （or full hydrodynamic） model for semiconductors, where the energy equation with non-zero thermal conductivity coefficient are contained, is discussed. The global existence of smooth solutions for the Cauchy problem with small perturbed initial data is proved. In particular, that the solutions converge to the corresponding stationary solutions exponentially fast as t → ∞ is showed.

关键词： asymptotic behavior global smooth solutions nonisentropic hydrodynamic model semiconductors