Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4610613 | Journal of Differential Equations | 2014 | 38 Pages |
Abstract
We study the Cauchy problem for multi-dimensional compressible radiation hydrodynamics equations with vacuum. First, we present some sufficient conditions on the blow-up of smooth solutions in multi-dimensional space. Then, we obtain the invariance of the support of density for the smooth solutions with compactly supported initial mass density by the property of the system under the vacuum state. Based on the above-mentioned results, we prove that we cannot get a global classical solution, no matter how small the initial data are, as long as the initial mass density is of compact support. Finally, we will see that some of the results that we obtained are still valid for the isentropic flows with degenerate viscosity coefficients as well as for one-dimensional case.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Yachun Li, Shengguo Zhu,