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On the stability of contact discontinuity for compressible Navier-Stokes equations with free boundary. (English) Zbl 1062.35066

The authors consider a free boundary problem for the one-dimensional compressible Navier-Stokes equations which, in Lagrangian coordinates, leads to a system on the positive half-line. The goal of the paper is to investigate the stability of a viscous contact discontinuity. Denoting by \(\theta_-\) the value of the temperature at \(x=0\) and by \(\theta_+\) the value as \(x\to\infty\) the authors prove that viscous contact discontinuities are asymptotically stable provided that \(|\theta_+-\theta_-|\) is sufficiently small. Perturbations decay uniformly in space as \(t\to\infty\).

MSC:

35Q30 Navier-Stokes equations
35R35 Free boundary problems for PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
80A20 Heat and mass transfer, heat flow (MSC2010)
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