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 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.
Citation
Xiangdi Huang. "On formation of singularity of spherically symmetric nonbarotropic flows." Kyoto J. Math. 55 (1) 1 - 15, April 2015. https://doi.org/10.1215/21562261-2801813