可压缩Navier-Stokes方程的球对称经典解

The classical solutions to the spherically symmetric compressible Navier-Stokes equations

可压缩Navier-Stokes方程反映着流体力学研究的前沿,为了对其Vaigant-Kazhikhov模型的解进行深入研究,借鉴并推广了相关文献关于二维方程密度估计的方法到三维球对称情形,证明了外区域中Cauchy问题的球对称经典解的适定性。证得当黏性系数λ(ρ)=ρβ时,β>14/5以及当初始密度远离真空状态时,解在有限时间段内也不会出现真空状态。

The compressible Navier-Stokes equations has an important position in the progress of fluid mechanics. In order to research the Vaigant-Kazhikhow model, the methods of related arti- cles in 2D are referenced and the results of the 3D spherically symmetric situation are obtained. It is proved that the global well-posedness of the classical solution to the Cauchy problem of spheri- cally symmetric compressible Navier-Stokes equations in an exterior domain. When the bulk vis- cosity λ（ρ）=ρB,β〉14/5 ,it is shown that the solution will not develop the vacuum states in any fi- nite time provided the initial density is uniformly away from vacuum.