Shuangqian Liu

Stability of the Rarefaction Wave of the Vlasov--Poisson--Boltzmann System

This paper is devoted to the study of the nonlinear stability of the rarefaction waves of the Vlasov--Poisson--Boltzmann system with slab symmetry in the case where the electron background density satisfies an analogue of the Boltzmann relation. We allow that the electric potential may take distinct constant states at both far fields. The rarefaction wave is constructed by the quasineutral Euler equations through the zero-order fluid dynamic approximation, and the wave strength is not necessarily small. We prove that the local Maxwellian with macroscopic quantities determined by the quasineutral rarefaction wave is time-asymptotically stable under small perturbations for the corresponding Cauchy problem. The main analytical tool is the combination of techniques we developed in [R.-J. Duan and S.-Q. Liu, J. Differential Equations, 258 (2015), pp. 2495--2530] for the viscous compressible fluid with the self-consistent electric field and the refined energy method based on the macro-micro decomposition of the...

The Initial Boundary Value Problem for the Boltzmann Equation with Soft Potential

Boundary effects are central to the dynamics of the dilute particles governed by the Boltzmann equation. In this paper, we study both the diffuse reflection and the specular reflection boundary value problems for the Boltzmann equation with a soft potential, in which the collision kernel is ruled by the inverse power law. For the diffuse reflection boundary condition, based on an L2 argument and its interplay with intricate

The Vlasov-Poisson-Boltzmann System without Angular Cutoff

{L^\infty}

Stability of rarefaction waves of the Navier–Stokes–Poisson system

L∞ analysis for the linearized Boltzmann equation, we first establish the global existence and then obtain the exponential decay in

Stability of the rarefaction wave for a two-fluid plasma model with diffusion

{L^\infty}

Global Well-Posedness in Spatially Critical Besov Space for the Boltzmann Equation

L∞ space for the nonlinear Boltzmann equation in general classes of bounded domain. It turns out that the zero lower bound of the collision frequency and the singularity of the collision kernel lead to some new difficulties for achieving the a priori