Communications in Mathematical Sciences

Volume 14 (2016)

Number 7

Stability of contact discontinuity for the Navier–Stokes–Poisson system with free boundary

Pages: 1859 – 1887

DOI: http://dx.doi.org/10.4310/CMS.2016.v14.n7.a4

Authors

Shuangqian Liu (Department of Mathematics, Jinan University, Guangzhou, China)

Haiyan Yin (School of Mathematical Sciences, Huaqiao University, Quanzhou, China)

Changjiang Zhu (School of Mathematics, South China University of Technology, Guangzhou, China)

Abstract

This paper is concerned with the study of the nonlinear stability of the contact discontinuity of the Navier–Stokes–Poisson system with free boundary in the case where the electron background density satisfies an analogue of the Boltzmann relation. We especially allow that the electric potential can take distinct constant states at boundary. On account of the quasineutral assumption, we first construct a viscous contact wave through the quasineutral Euler equations and then prove that such a non-trivial profile is time-asymptotically stable under small perturbations for the corresponding initial boundary value problem of the Navier–Stokes–Poisson system. The analysis is based on an elementary energy method.

Keywords

viscous contact discontinuity, quasineutral Euler equations, stability, free boundary

2010 Mathematics Subject Classification

35B35, 35Q35, 82D10

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Published 14 September 2016