On solvability and ill-posedness of the compressible Euler system subject to stochastic forces

Dominic Breit, Eduard Feireisl, Martina Hofmanová

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1 Citation (Scopus)
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Abstract

We consider the barotropic Euler system describing the motion of a compressible inviscid fluid driven by a stochastic forcing. Adapting the method of convex integration we show that the initial value problem is ill-posed in the class of weak (distributional) solutions. Specifically, we find a sequence τM→∞ of positive stopping times for which the Euler system admits infinitely many solutions originating from the same initial data. The solutions are weak in the PDE sense but strong in the probabilistic sense, meaning, they are defined on an a priori given stochastic basis and adapted to the driving stochastic process.
Original languageEnglish
Pages (from-to)371–402
Number of pages32
JournalAnalysis and PDE
Volume13
Issue number2
DOIs
Publication statusPublished - 19 Mar 2020

Keywords

  • Compressible euler system
  • Convex integration
  • Ill-posedness
  • Stochastic compressible euler system
  • Stochastic forcing
  • Weak solution

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

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