Amplitude blowup in radial isentropic Euler flow. (English) Zbl 1456.35046
The authors consider inviscid isentropic flow described by the compressible Euler system in 2 or 3 spatial dimensions. An additional assumption of symmetry is made: velocity is radial, and all variables depend on the distance to the origin. The aim is to prove the possibility of unbounded solutions due to wave focusing possible in several spatial dimensions.
Reviewer: Ilya A. Chernov (Petrozavodsk)
MSC:
| 35B44 | Blow-up in context of PDEs |
| 35L45 | Initial value problems for first-order hyperbolic systems |
| 35L65 | Hyperbolic conservation laws |
| 35L67 | Shocks and singularities for hyperbolic equations |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 35Q31 | Euler equations |
Keywords:
compressible fluid flow; multi-d isentropic Euler system; similarity solutions; radial symmetry; unbounded solutions; wave focusingReferences:
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