一维可压缩Navier-Stokes方程初值问题强解的整体存在性

Existence of Global Strong Solutions for the Initial Value Problem of One-dimensional Compressible Navier-Stokes Equations

考虑粘性系数依赖于密度的一维等熵可压缩Navier-Stokes方程.利用等价变换和抛物方程的极值原理得到密度函数的正下界,再结合其他能量估计得到密度的上界,从而证明真空和集中状态都不会产生.通过修改粘性系数法构造逼近解,并结合密度的先验下界估计得到强解的整体存在性.

This paper is concerned with the isentropic compressible Navier-Stokes equations with density-dependent viscosity in one dimensional space.The positive lower bound of density function is obtained by using equivalent transformation and the maximum principle of parabolic equation.Combined with other energy estimates,the upper bound on the density is got.It turns out that neither a vacuum nor a concentrated state can occur.The existence of global strong solution is obtained by the approximation with the modification of the viscosity and using the a priori lower bound of the density.