A remark on free boundary problem of 1-D compressible Navier-Stokes equations with density-dependent viscosity

作者：Dou, Changsheng; Jiu, Quansen^*

来源：Mathematical Methods in the Applied Sciences, 2010, 33(1): 103-116.

DOI：10.1002/mma.1154

• compressible Navier-Stokes equations
• free boundary problem
• weak solutions
• existence and uniqueness

In this paper, we prove the existence and uniqueness of the weak solution of the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity pi(rho) = rho(theta) with 0 is an element of (0, gamma/2], gamma > 1. The initial data are a perturbation of a corresponding steady solution and continuously contact with vacuum on the free boundary. The obtained results apply for the one-dimensional Siant-Venant model of shallow water and generalize ones in (Arch. Rational Mech. Anal. 2006; 182: 223-253).

• 出版日期2010-1-15
• 单位首都师范大学