Global Well-posedness of Classical Solutions to the Compressible Navier-Stokes-Poisson Equations with Slip Boundary Conditions in 3D Bounded Domains

TL;DR

This paper proves the global existence and uniqueness of classical solutions to the 3D compressible Navier-Stokes-Poisson equations with slip boundary conditions, even with large initial oscillations and vacuum, in bounded domains.

Contribution

It establishes the first global well-posedness result for these equations under large variation in doping profiles and vacuum conditions with slip boundaries.

Findings

Global classical solutions exist under small initial energy.

Solutions can handle large oscillations and vacuum states.

Steady states and doping profiles can vary significantly.

Abstract

We consider the initial-boundary-value problem of the isentropic compressible Navier-Stokes-Poisson equations subject to large and non-flat doping profile in 3D bounded domain with slip boundary condition and vacuum. The global well-posedness of classical solution is established with small initial energy but possibly large oscillations and vacuum. The steady state (except velocity) and the doping profile are allowed to be of large variation.