论文标题
在3D有界域中具有大振荡和真空的完全可压缩Navier-Stokes系统的经典解决方案的全球存在
Global Existence of Classical Solutions to Full Compressible Navier-Stokes System with Large Oscillations and Vacuum in 3D Bounded Domains
论文作者
论文摘要
完整的可压缩Navier-Stokes系统，描述了粘性，可压缩，热传导性和牛顿多变态流体的运动，在三维简单连接的有界结构域中具有平滑边界，具有有限数量的二维连接组件。对于在速度和温度下的Neumann边界上有滑动边界条件的初始边界问题，在温度下，经典和弱解决方案的全球存在是较小的，但可能建立了较大的振荡。特别是，最初允许密度和温度消失。最后，还获得了密度，速度和温度的指数稳定性。此外，可以证明，对于经典的解决方案，从长远来看，密度的振荡将在最初（即使在某个点上）出现，从长远来看将无限制地生长。这是关于整体存在对完整可压缩的Navier-Stokes方程的经典解决方案的结果，该方程在一般的三维边界平滑域中具有真空。
The full compressible Navier-Stokes system describing the motion of a viscous, compressible, heat-conductive, and Newtonian polytropic fluid is studied in a three-dimensional simply connected bounded domain with smooth boundary having a finite number of two-dimensional connected components. For the initial-boundary-value problem with slip boundary conditions on the velocity and Neumann boundary one on the temperature, the global existence of classical and weak solutions which are of small energy but possibly large oscillations is established. In particular, both the density and temperature are allowed to vanish initially. Finally, the exponential stability of the density, velocity, and temperature is also obtained. Moreover, it is shown that for the classical solutions, the oscillation of the density will grow unboundedly in the long run with an exponential rate provided vacuum appears (even at a point) initially. This is the first result concerning the global existence of classical solutions to the full compressible Navier-Stokes equations with vacuum in general three-dimensional bounded smooth domains.
