Stability of steady states of the 3-D Navier-Stokes-Poisson equations with non-flat doping profile in exterior domains

TL;DR

This paper proves the global stability of steady states for the 3-D compressible Navier-Stokes-Poisson equations with non-flat doping profiles in exterior domains, using advanced boundary and elliptic estimates.

Contribution

It establishes the existence and stability of steady states in a complex exterior domain setting with non-flat doping, employing novel a priori and elliptic boundary estimates.

Findings

Global existence of strong solutions near steady states

Construction of steady states via sub and super solution method

Development of new a priori estimates for boundary and elliptic problems

Abstract

This paper concerns an initial boundary value problem of compressible Navier-Stokes-Poisson equations with the non-flat doping profile in a 3-D exterior domain.The global existence of strong solutions near a steady state for compressible Navier-Stokes-Poisson equations with the general Navier-slip boundary conditions is established. For our setting, not only a steady state should be constructed in the exterior domain by the sub and super solution method, but also some new techniques should be adopted to obtain a priori estimates, especially some refined elliptic estimates and the estimates on the boundary.