Global classical solution of the Cauchy problem to 1D compressible Navier-Stokes equations with large initial data

作者：Jiu, Quansen; Li, Mingjie; Ye, Yulin^*

来源：Journal of Differential Equations, 2014, 257(2): 311-350.

DOI：10.1016/j.jde.2014.03.014

• Compressible Navier-Stokes equations
• Density-dependent viscosity
• Global classical solution
• Vacuum
• Weighted estimates

In this paper, we prove that the 1D Cauchy problem of the compressible Navier-Stokes equations admits a unique global classical solution (rho, u) if the viscosity,mu(rho) = 1 + rho(beta) with beta >= 0. The initial data can be arbitrarily large and may contain vacuum. Some new weighted estimates of the density and velocity are obtained when deriving higher order estimates of the solution.

• 出版日期2014-7-15
• 单位首都师范大学; 中央民族大学