On the blow-up phenomena of solutions for the full compressible Euler equations in \(\mathbb{R}^N\). (English) Zbl 1359.35141
Summary: In fluid dynamics, blow-up phenomena of solutions is interesting and challenging to physicists and mathematicians. The present paper is devoted to studying blow-up phenomena of the spherically symmetric solutions for the full compressible Euler equations in \(\mathbb{R}^N,N\geqslant1\). The approach is to a construct special explicit solution with spherical symmetry to study certain blow-up phenomena of solutions to the full compressible Euler equation in \(\mathbb{R}^N\). We also discuss steady-state smooth solutions of spherical symmetry to equation (1.1).
MSC:
| 35Q31 | Euler equations |
| 35L45 | Initial value problems for first-order hyperbolic systems |
| 35L65 | Hyperbolic conservation laws |
| 35B44 | Blow-up in context of PDEs |
| 35B06 | Symmetries, invariants, etc. in context of PDEs |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 76N99 | Compressible fluids and gas dynamics |
Keywords:
the full compressible Euler equations; blow-up phenomena; spherically symmetric solutions; steady-state smooth solutionsReferences:
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