Formation of Unstable Shocks for 2D Isentropic Compressible Euler

Tristan Buckmaster, Sameer Iyer

Research output: Contribution to journalArticlepeer-review

Abstract

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 C15 self-similar solution to the Burgers’ equation. Moreover, we show the behavior is stable in C8 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.

Original languageEnglish (US)
Pages (from-to)197-271
Number of pages75
JournalCommunications In Mathematical Physics
Volume389
Issue number1
DOIs
StatePublished - Jan 2022

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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