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arXiv · 1907.13403

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

Dongfen Bian·Jinkai Li
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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 $\mathbb R^N$, with $N\geq1$. We prove that any classical solutions $(\rho, u, \theta)$, in the class $C^1([0,T]; H^m(\Omega))$, $m>[\frac N2]+2$, 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 reault by Xin [CPAM, 1998], in which the Cauchy probelm is considered, to the case that with physical boundary.

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Dongfen Bian, Jinkai Li. 2019-07-31. Finite time blow up of compressible Navier-Stokes equations on half space or outside a fixed ball. https://arxiv.org/abs/1907.13403

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