Stability of the Superposition of a Viscous Contact Wave with two Rarefaction Waves to the bipolar Vlasov-Poisson-Boltzmann System

TL;DR

This paper proves the nonlinear stability of a combined wave pattern (viscous contact wave and two rarefaction waves) in a 1D bipolar Vlasov-Poisson-Boltzmann system, considering collisions, electrostatic forces, and particle interactions.

Contribution

It introduces a new micro-macro decomposition approach and demonstrates the first nonlinear stability result for combined wave patterns in the VPB system.

Findings

Superposition of waves is asymptotically stable under small perturbations.

Stability holds despite complex interactions of collisions and electrostatic forces.

First such stability result for combined wave patterns in VPB system.

Abstract

We investigate the nonlinear stability of the superposition of a viscous contact wave and two rarefaction waves for one-dimensional bipolar Vlasov-Poisson-Boltzmann (VPB) system, which can be used to describe the transportation of charged particles under the additional electrostatic potential force. Based on a new micro-macro type decomposition around the local Maxwellian related to the bipolar VPB system in our previous work [26], we prove that the superposition of a viscous contact wave and two rarefaction waves is time-asymptotically stable to 1D bipolar VPB system under some smallness conditions on the initial perturbations and wave strength, which implies that this typical composite wave pattern is nonlinearly stable under the combined effects of the binary collisions, the electrostatic potential force, and the mutual interactions of different charged particles. Note that this is the first result about the nonlinear stability of the combination of two different wave patterns for the Vlasov-Poisson-Boltzmann system.