Formation of Unstable Shocks for 2D Isentropic Compressible Euler

Tristan Buckmaster, Sameer Iyer

Research output: Contribution to journalArticlepeer-review


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
Issue number1
StatePublished - Jan 2022

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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