Global Solutions to the initial boundary problem of 3-D compressible Navier-Stokes-Poisson on bounded domains

TL;DR

This paper proves the global existence and exponential stability of smooth solutions to the 3-D compressible Navier-Stokes-Poisson equations on bounded domains, allowing large variations in steady states and background profiles.

Contribution

It establishes the first global existence and stability results for these equations with large variation in steady states on bounded domains.

Findings

Global smooth solutions exist near steady states.

Solutions exhibit exponential stability.

Results accommodate large variations in steady states.

Abstract

The initial boundary value problems for compressible Navier-Stokes-Poisson is considered on a bounded domain in $\mathbb{R}^3$ in this paper. The global existence of smooth solutions near a given steady state for compressible Navier-Stokes-Poisson with physical boundary conditions is established with the exponential stability. An important feature is that the steady state (except velocity) and the background profile are allowed to be of large variation.