Singular Limits for the Navier-Stokes-Poisson Equations of Viscous Plasma with Strong Density Boundary Layer

TL;DR

This paper rigorously analyzes the quasi-neutral limit of the Navier-Stokes-Poisson system for viscous plasma in a half-space, focusing on boundary layer interactions and stability under specific boundary conditions.

Contribution

It establishes the nonlinear stability of approximation solutions involving strong boundary layers in density and electric potential, addressing boundary layer interactions.

Findings

Proved the quasi-neutral limit rigorously for viscous plasma in half-space.

Established nonlinear stability of boundary layer solutions.

Analyzed the interaction between strong density boundary layer and weak velocity boundary layer.

Abstract

The quasi-neutral limit of the Navier-Stokes-Poisson system modeling a viscous plasma with vanishing viscosity coefficients in the half-space $\mathbb{R}^{3}_{+}$ is rigorously proved under a Navier-slip boundary condition for velocity and the Dirichlet boundary condition for electric potential. This is achieved by establishing the nonlinear stability of the approximation solutions involving the strong boundary layer in density and electric potential, which comes from the break-down of the quasi-neutrality near the boundary, and dealing with the difficulty of the interaction of this strong boundary layer with the weak boundary layer of the velocity field.