Stability of viscous shock waves for the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity. (English) Zbl 1363.35034
Summary: We study the large-time behavior toward viscous shock waves to the Cauchy problem of the one-dimensional compressible isentropic Navier-Stokes equations with density-dependent viscosity. The nonlinear stability of the viscous shock waves is shown for certain class of large initial perturbation with integral zero which can allow the initial density to have large oscillation. Our analysis relies upon the continuation argument.
MSC:
35B35 | Stability in context of PDEs |
35Q30 | Navier-Stokes equations |
76L05 | Shock waves and blast waves in fluid mechanics |
76N15 | Gas dynamics (general theory) |