Global smooth solutions of the compressible Navier-Stokes equations with density-dependent viscosity

作者：Qin, Xulong^*; Yao, Zheng an

来源：Journal of Differential Equations, 2008, 244(8): 2041-2061.

DOI：10.1016/j.jde.2007.11.001

• Navier-Stokes equations
• density-dependent viscosity
• global existence

In this paper we study a free boundary problem for the viscous, compressible, heat conducting, one-dimensional real fluids. More precisely, the viscosity is assumed to be a power function of density, i.e., mu (rho) = rho(alpha), where rho denotes the density of fluids and a is a positive constant. In addition, the equations of state include and are more general than perfect flows which only depend linearly on temperature. The global existence (uniqueness) of smooth solutions is established with alpha is an element of(0, 1/2] for general, large initial data, which improves the previous results. Moreover, it is also shown that the solutions will not develop vacuum, mass concentration or heat concentration in a finite time provided the initial data are bounded and smooth, and do not contain vacuum.

• 出版日期2008-4-15
• 单位中山大学