Open Access
April 2015 On formation of singularity of spherically symmetric nonbarotropic flows
Xiangdi Huang
Kyoto J. Math. 55(1): 1-15 (April 2015). DOI: 10.1215/21562261-2801813


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 for the breakdown of the classical solution. For smooth initial data away from vacuum, we prove that the classical solution which is spherically symmetric loses its regularity in a finite time if and only if the density concentrates or vanishes or the 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. "On formation of singularity of spherically symmetric nonbarotropic flows." Kyoto J. Math. 55 (1) 1 - 15, April 2015.


Published: April 2015
First available in Project Euclid: 13 March 2015

zbMATH: 06434628
MathSciNet: MR3323524
Digital Object Identifier: 10.1215/21562261-2801813

Primary: 35Q30
Secondary: 76N10

Rights: Copyright © 2015 Kyoto University

Vol.55 • No. 1 • April 2015
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