Huang, Feimin; Matsumura, Akitaka; Shi, Xiaoding On the stability of contact discontinuity for compressible Navier-Stokes equations with free boundary. (English) Zbl 1062.35066 Osaka J. Math. 41, No. 1, 193-210 (2004). 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 \(t\to\infty\). Reviewer: Klaus Deckelnick (Magdeburg) Cited in 2 ReviewsCited in 39 Documents 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) Keywords:free boundary problem for the one-dimensional compressible Navier-Stokes equations; viscous contact discontinuity; asymptotic stability PDFBibTeX XMLCite \textit{F. Huang} et al., Osaka J. Math. 41, No. 1, 193--210 (2004; Zbl 1062.35066)