Formation of Unstable Shocks for 2D Isentropic Compressible Euler
| Autor: | Tristan Buckmaster, Sameer Iyer |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Physics
010102 general mathematics Mathematical analysis Order (ring theory) Statistical and Nonlinear Physics Context (language use) 01 natural sciences Linear subspace Stability (probability) Manifold Symmetry (physics) symbols.namesake Mathematics - Analysis of PDEs 0103 physical sciences FOS: Mathematics Compressibility Euler's formula symbols 010307 mathematical physics 0101 mathematics Mathematical Physics Analysis of PDEs (math.AP) |
| Zdroj: | Communications in Mathematical Physics. 389:197-271 |
| ISSN: | 1432-0916 0010-3616 |
| DOI: | 10.1007/s00220-021-04271-z |
| Popis: | In this paper we construct unstable shocks in the context of 2D isentropic compressible Euler in azimuthal symmetry. More specifically, we construct initial data that when viewed in self-similar coordinates, converges asymptotically to the unstable $C^{\frac15}$ self-similar solution to the Burgers' equation. Moreover, we show the behavior is stable in $C^8$ modulo a two dimensional linear subspace. Under the azimuthal symmetry assumption, one cannot impose additional symmetry assumptions in order to isolate the corresponding manifold of initial data leading to stability: rather, we rely on modulation variable techniques in conjunction with a Newton scheme. 68 pages, accepted version |
| Databáze: | OpenAIRE |
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