Stability of rarefaction waves for the non-cutoff Vlasov-Poisson-Boltzmann system with physical boundary

In this paper, we are concerned with the Vlasov-Poisson-Boltzmann (VPB) system in three-dimensional spatial space without angular cutoff in a rectangular duct with or without physical boundary conditions. Near a local Maxwellian with macroscopic quantities given by rarefaction wave solution of one-dimensional compressible Euler equations, we establish the time-asymptotic stability of planar rarefaction wave solutions for the Cauchy problem to VPB system with periodic or specular-reflection boundary condition. In particular, we successfully introduce physical boundaries, namely, specular-reflection boundary, to the models describing wave patterns of kinetic equations. Moreover, we treat the non-cutoff collision kernel instead of the cutoff one. As a simplified model, we also consider the stability and large time behavior of the rarefaction wave solution for the Boltzmann equation.(c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This paper discusses the time-asymptotic stability of planar rarefaction wave solutions for the Vlasov-Poisson-Boltzmann (VPB) system in a three-dimensional rectangular duct without angular cutoff. The system is studied with periodic or specular-reflection boundary conditions, and physical boundaries are introduced to describe wave patterns of kinetic equations. The non-cutoff collision kernel is considered, and the stability and large time behavior of the rarefaction wave solution for the Boltzmann equation are also examined.