Finite time blow up of compressible Navier-Stokes equations on half space or outside a fixed ball

[摘要] 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 (rho, u, theta), in the class C-1 ([0, T]; H-m (Omega)), 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. (C) 2019 Elsevier Inc. All rights reserved.

[发布日期] 2019-12-05

[关键词] Compressible Navier-Stokes equations;Finite time blow up;Classical solutions