Optimal convergence rate of the vanishing shear viscosity limit for compressible Navier-Stokes equations with cylindrical symmetry

作者：Wen, Huanyao; Yang, Tong^*; Zhao, Xinhua; Zhu, Changjiang

来源：Journal des Mathematiques Pures et Appliquees, 2021, 146: 99-126.

DOI：10.1016/j.matpur.2020.09.003

• Compressible Navier-Stokes equations
• Boundary layer
• Global stability
• Vanishing shear viscosity

We consider the initial boundary value problem for the isentropic compressible Navier-Stokes equations with cylindrical symmetry. The existence of boundary layers is well-known when the shear viscosity vanishes. In this paper, we derive explicit Prandtl type boundary layer equations and prove the global in time stability of the boundary layer profile together with the optimal convergence rate of the vanishing shear viscosity limit without any smallness assumption on the initial and boundary data.

• 单位
  重庆大学