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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)
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