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 Initial Value Problems 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方程的初值问题.利用能量估计得到密度的上界和下界,从而证明了真空和集中状态都不会产生.再利用关于强解的局部存在性结论,通过变换粘性系数构造逼近解,并结合密度和速度的先验估计得到强解的整体存在性.

To consider the initial problem for one-dimensional compressible isentropic Navier-Stokes equations with density-dependent viscosity.By using the energy estimates,the lower and upper bounds for the density is derived,that is,nether vacuum states nor concentration states can occur.Finally,the approximate solution is constructed by transforming the viscous coefficient,the existence of global strong solution is obtained by using the local existence conclusion of the strong solution and combining a prior estimates of the density function and the velocity function.