Large-time behavior of solutions to the outflow problem for the compressible Navier-Stokes-Maxwell equations

TL;DR

This paper proves the nonlinear stability of combined boundary layer and rarefaction waves for the outflow problem in the compressible Navier-Stokes-Maxwell equations, incorporating electrodynamic effects into the large-time behavior analysis.

Contribution

It is the first to establish the nonlinear stability of combined wave patterns for the IBVP of the non-isentropic Navier-Stokes-Maxwell equations, considering electrodynamic effects.

Findings

Composite wave pattern is time-asymptotically stable.

Stability holds under smallness conditions and bounded dielectric constant.

Includes electrodynamic effects into the stability analysis.

Abstract

We investigate the large-time behavior of solutions toward the combination of the boundary layer and 3-rarefaction waves to the outflow problem for the compressible non-isentropic Navier-Stokes equations coupling with the Maxwell equations through the Lorentz force (called the Navier-Stokes-Maxwell equations) on the half line $ \mathbb{R}_+ $. It includes the electrodynamic effects into the dissipative structure of the hyperbolic-parabolic system and turns out to be more complicated than that in the simpler compressible Navier-Stokes equations. We prove that this typical composite wave pattern is time-asymptotically stable with the composite boundary condition of the electromagnetic fields, under some smallness conditions and the assumption that the dielectric constant is bounded. This can be viewed as the first result about the nonlinear stability of the combination of two different wave patterns for the IBVP of the non-isentropic Navier-Stokes-Maxwell equations.