Finite time blow up of compressible Navier-Stokes equations on half space or outside a fixed ball
Finite time blow up of compressible Navier-Stokes equations on half space or outside a fixed ball
复制标题
DOI：
10.1016/j.jde.2019.07.008
复制
发表时间：
2019-07
影响因子：
2.4
通讯作者：
Dongfen Bian;Jinkai Li
中科院分区：
文献类型：
--
作者：
Dongfen Bian;Jinkai Li
在本文中，我们考虑了在 R N 的半空间或固定球外部没有热传导的理想气体的可压缩纳维-斯托克斯方程的初始边值问题，其中 N≥ 1。我们证明了任何经典解 (ρ, u, θ)，在 C 1 ([0, T]; H m (Ω)) 类中，m>[N 2]+ 2，其下限为初始熵和紧支持的初始密度，这允许要触及物理边界，只要初始质量为正，就必须在有限时间内爆炸。本文将Xin(1998)[19]考虑柯西问题的经典结果推广到有物理边界的情况。
In this paper, we consider the initial-boundary value problem to the compressible Navier-Stokes equations for ideal gases without heat conduction in the half space or outside a fixed ball in R N, with N≥ 1. We prove that any classical solutions (ρ, u, θ), in the class C 1 ([0, T]; H m (Ω)), m>[N 2]+ 2, with bounded from below initial entropy and compactly supported initial density, which allows to touch the physical boundary, must blow-up in finite time, as long as the initial mass is positive. This paper extends the classical result by Xin (1998)[19], in which the Cauchy problem is considered, to the case that with physical boundary.