Stability of rarefaction waves of the Navier-Stokes-Poisson system

Abstract

In the paper we are concerned with the large time behavior of solutions to the one-dimensional Navier-Stokes-Poisson system in the case when the potential function of the self-consistent electric field may take distinct constant states at $x=\pm \infty$. Precisely, it is shown that if initial data are close to a constant state with asymptotic values at far fields chosen such that the Riemann problem on the corresponding quasineutral Euler system admits a rarefaction wave whose strength is not necessarily small, then the solution exists for all time and tends to the rarefaction wave as $t\to +\infty$. The construction of the nontrivial large-time profile of the potential basing on the quasineutral assumption plays a key role in the stability analysis. The proof is based on the energy method by taking into account the effect of the self-consistent electric field on the viscous compressible fluid.

26 pages. Accepted for publication in J. Differential Equations

References in corpus (1)

• Decay structure for symmetric hyperbolic systems with non-symmetric relaxation and its application

Cited by in corpus (1)

• Global stability of the rarefaction wave of the Vlasov-Poisson-Boltzmann system