Singularity formation for radially symmetric expanding wave of compressible Euler equations. (English) Zbl 1522.35380
Summary: In this paper, for compressible Euler equations in multiple space dimensions, we prove the breakdown of classical solutions with a large class of initial data by tracking the propagation of radially symmetric expanding wave including compression. The singularity formation considered in this paper is corresponding to the finite time shock formation. We also provide some new global sup-norm estimates on velocity and density functions for classical solutions and construct the corresponding classical solutions. All results in this paper have no restriction on the size of solutions and hence are large data results.
MSC:
| 35Q31 | Euler equations |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 76N15 | Gas dynamics (general theory) |
| 76L05 | Shock waves and blast waves in fluid mechanics |
| 76J20 | Supersonic flows |
| 35L65 | Hyperbolic conservation laws |
| 35L67 | Shocks and singularities for hyperbolic equations |
| 35B06 | Symmetries, invariants, etc. in context of PDEs |
| 35A09 | Classical solutions to PDEs |
| 35B44 | Blow-up in context of PDEs |
Keywords:
singularity formation; shock; compressible Euler equations; radially symmetric solution; supersonic flowsReferences:
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