In this paper we establish the convergence of the Vlasov-Poisson-Boltzmann system to the incompressible Euler equations in the so-called quasi-neutral regime. The convergence is rigorously proved for time intervals on which the smooth solution of the Euler equations of the incompressible fluid exists. The proof relies on the relative-entropy method.
We establish the convergence of the Vlasov-Poisson-Fokker-Planck system to the incompressible Euler equations in this paper. The convergence is rigorously proved on the time interval where the smooth solution to the incompressible Euler equations exists. The proof relies on the compactness argument and the so-called relative-entropy method.
XIAO Ling, LI Fucai & WANG Shu Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China
In this paper, the convergence compressible Euler-Poisson equations in a of time-dependent Euler-Maxwell equations to torus via the non-relativistic limit is studied. The local existence of smooth solutions to both systems is proved by using energy estimates for first order symmetrizable hyperbolic systems. For well prepared initial data the convergence of solutions is rigorously justified by an analysis of asymptotic expansions up to any order. The authors perform also an initial layer analysis for general initial data and prove the convergence of asymptotic expansions up to first order.
In this paper, we obtain the necessary and sufficient conditions on the global existence of all positive （weak） solutions to a nonlinear degenerate parabolic equation with nonlinear boundary condition.
