Nonlinear stability of viscous shock profiles for compressible Navier-Stokes equations with temperature-dependent transport coefficients and large initial perturbation

作者：Huang, Bingkang; Tang, Shaojun; Zhang, Lan^*

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2018, 69(6): 136.

DOI：10.1007/s00033-018-1026-6

• One-dimensional compressible Navier-Stokes equations
• Temperature-dependent transport coefficients
• Viscous shock profiles
• Global stability
• Large initial perturbation

We study the nonlinear stability of viscous shock profiles of the Cauchy problem to the one-dimensional compressible Navier-Stokes equations for a viscous and heat-conducting ideal polytropic gas whose transport coefficients depend on both the density and temperature. The viscous shock profiles are shown to be asymptotically stable under large initial perturbation when the adiabatic exponent. is suitably close to 1, and the strengths of the viscous shock profiles are sufficiently small which allow initial density to have large oscillation. The crucial step in the energy estimates is to obtain uniformly positive lower and upper bounds of density.

• 出版日期2018-12
• 单位合肥工业大学; 武汉大学