Local and global existence of smooth solutions for the stochastic euler equations with multiplicative noise

Nathan E. Glatt-Holtz, Vlad C. Vicol

Research output: Contribution to journalArticle

33 Scopus citations

Abstract

We establish the local existence of pathwise solutions for the stochastic Euler equations in a three-dimensional bounded domain with slip boundary conditions and a suitable nonlinear multiplicative noise. In the twodimensional case we obtain the global existence of these solutions with additive or linear-multiplicative noise. Finally, we show that, in the threedimensional case, the addition of linear multiplicative noise provides a regularizing effect; the global existence of solutions occurs with high probability if the initial data is sufficiently small, or if the noise coefficient is sufficiently large.

Original languageEnglish (US)
Pages (from-to)80-145
Number of pages66
JournalAnnals of Probability
Volume42
Issue number1
DOIs
StatePublished - Jan 1 2014

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Compactness methods
  • Euler equations
  • Nonlinear multiplicative noise
  • Pathwise solutions
  • Stochastic partial differential equations on lebesgue spaces

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