Asymptotic stability of nonlinear wave for the compressible Navier-Stokes equations in the half space. (English) Zbl 1149.35011
The authors consider the initial-boundary value problem for the one-dimensional isentropic compressible Navier-Stokes equations in the half space. The problem is the outflow problem, i.e.the velocity on the bound is negative. The focus is at the large-time behaviour of the solution. The space-symptotic states and the boundary data are assumed to satisfy sertain condition so that the solution is a nonlinear wave which is the superposition of a stationary solution and a rarefaction wave. It is proved that this wave is nonlinearly stable under small perturbations.
Reviewer: Ilya A. Chernov (Petrozavodsk)
MSC:
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35B35 | Stability in context of PDEs |
| 76N15 | Gas dynamics (general theory) |
| 35L70 | Second-order nonlinear hyperbolic equations |
| 35Q30 | Navier-Stokes equations |
Keywords:
superposition of a rarefaction wave and a stationary solution; Eulerian coordinates; half-space initial-boundary value problem; one space dimension; large-time behaviourReferences:
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