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Finite time blow up of compressible Navier-Stokes equations on half space or outside a fixed ball.
- Source :
-
Journal of Differential Equations . Dec2019, Vol. 267 Issue 12, p7047-7063. 17p. - Publication Year :
- 2019
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 267
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 138853476
- Full Text :
- https://doi.org/10.1016/j.jde.2019.07.008