Stability of rarefaction waves for the non-cutoff Vlasov–Poisson–Boltzmann system with physical boundary. (June 2023)

• Record Type: Journal Article
• Authors: Deng, Dingqun
• Is Part Of: Nonlinear analysis. Volume 71(2023)
• Publication Date: 2023-06
• Subjects: Wave patterns -- Rarefaction wave -- Vlasov–Poisson–Boltzmann system -- Boltzmann equation -- Specular boundary condition; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103806
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: 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.