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arXiv · 1403.2520

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

Renjun Duan·Shuangqian Liu
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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.

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Renjun Duan, Shuangqian Liu. 2014-03-11. Stability of rarefaction waves of the Navier-Stokes-Poisson system. https://arxiv.org/abs/1403.2520

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