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arXiv · 1501.00109

On Formation of Singularity of Spherically Symmetric Nonbarotropic Flows

Xiangdi Huang
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Abstract

We study an initial boundary value problem on a ball for the heat-conductive system of compressible Navier-Stokes-Fourier equations, in particular, a criterion of breakdown of the classical solution. For smooth initial data away from vacuum, it is proved that the classical solution which is spherically symmetric loses its regularity in a finite time if and only if the {\bf density} {\it concentrates} or {\it vanishes} or the {\bf velocity} becomes unbounded around the center. One possible situation is that a vacuum ball appears around the center and the density may concentrate on the boundary of the vacuum ball simultaneously.

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Xiangdi Huang. 2014-12-31. On Formation of Singularity of Spherically Symmetric Nonbarotropic Flows. https://doi.org/10.1088/0004-6256%2F150%2F1%2F1

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