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Stability of the superposition of rarefaction wave and contact discontinuity for the non-isentropic Navier-Stokes-Poisson system. (English) Zbl 1367.35127
Summary: This paper is devoted to the study of the nonlinear stability of the composite wave consisting of a rarefaction wave and a viscous contact discontinuity wave of the non-isentropic Navier-Stokes-Poisson system with free boundary. We first construct the composite wave through the quasineutral Euler equations and then prove that the composite wave is time asymptotically stable under small perturbations for the corresponding initial-boundary value problem of the non-isentropic Navier-Stokes-Poisson system. Only the strength of the viscous contact wave is required to be small. However, the strength of the rarefaction wave can be arbitrarily large. In our analysis, the domain decomposition plays an important role in obtaining the zero-order energy estimates. By introducing this technique, we successfully overcome the difficulty caused by the critical terms involved with the linear term, which does not satisfy the quasineural assumption for the composite wave.

MSC:
35Q35 PDEs in connection with fluid mechanics
35B35 Stability in context of PDEs
82D10 Statistical mechanical studies of plasmas
35Q31 Euler equations
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35B40 Asymptotic behavior of solutions to PDEs
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
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