题目：Vanishing Viscosity Limit of the Navier-Stokes Equations to the Euler Equations for Compressible Fluid Flow with vacuum
摘要：We establish the vanishing viscosity limit of the Navier-Stokes equations to the Euler equations for three-dimensional compressible isentropic flow in the whole space. When the viscosity coefficients are given as constant multiples of the density's power，it is shown that there exists a unique regular solution of compressible Navier-Stokes equations with arbitrarily large initial data and vacuum, whose life span is uniformly positive in the vanishing viscosity limit. Via introducing a ``quasi-symmetric hyperbolic"--``degenerate elliptic" coupled structure to control the behavior of the velocity of the fluid near the vacuum, we establish some uniform estimates which lead the strong convergence of the regular solution of the viscous flow to that of the inviscid flow, we also give the rate of convergence. Furthermore, we point out that our framework is also applicable to other physical dimensions, say 1 and 2, with some minor modifications. This is a joint work with Yongcai Geng and Shengguo Zhu.