Stability of steady states of the Navier-Stokes-Poisson equations with non-flat doping profile

TL;DR

This paper investigates the stability of steady states in the Navier-Stokes-Poisson equations with varying doping profiles, establishing conditions for global existence and decay rates of solutions.

Contribution

It provides new results on the stability and decay behavior of solutions for large and small doping profiles in the Navier-Stokes-Poisson system.

Findings

Global existence of classical solutions near steady states for large doping profiles.

Time decay rates of solutions for small doping profiles with initial perturbations in L^p.

Conditions under which solutions remain stable or decay over time.

Abstract

We consider the stability of the steady state of the compressible Navier-Stokes-Poisson equations with the non-flat doping profile. We prove the global existence of classical solutions near the steady state for the large doping profile. For the small doping profile, we prove the time decay rates of the solution provided that the initial perturbation belongs to $L^p$ with $1\le p< 3/2$.