黏性系数依赖密度型可压缩Navier-Stokes 方程的零耗散极限问题

本文考虑黏性系数依赖密度的可压缩Navier-Stokes 方程解的零耗散极限问题. 假定Euler 方程的稀疏波解一端被真空状态连接, 我们证明Navier-Stokes 方程存在一列(依赖黏性的) 整体解, 且随着粘性的消失, 此整体解逐渐稳定于Euler 方程对应的稀疏波解和真空状态; 并且得到了一致衰减率估计. 此结果推广了常黏性系数的情形.

Zero dissipation limit of the rarefaction wave with vacuum for the compressible Navier-Stokes equations with density-dependent viscosity

In this paper, we study the zero dissipation limit of soutions co the compresssible Stokes equations with density-dependent viscosity ∈（p） = ∈p^α. Given a rarefaction wave with one-side vacuum state to the compressible Euler equations, we prove that the Navier-Stokes equations admit a sequence of global solutions, which converge to the above rarefaction and vacuum as the viscosity tends toward zero. Moreover, some decay rates depending on a with respect to viscosity e are obtained.