Dissipative Solutions to the Stochastic Euler Equations

Dominic Breit, Thamsanqa C. Moyo

Research output: Contribution to journalArticlepeer-review

Abstract

We study the three-dimensional incompressible Euler equations subject to stochastic forcing. We develop a concept of dissipative martingale solutions, where the nonlinear terms are described by generalised Young measures. We construct these solutions as the vanishing viscosity limit of solutions to the corresponding stochastic Navier–Stokes equations. This requires a refined stochastic compactness method incorporating the generalised Young measures. As a main novelty, our solutions satisfy a form of the energy inequality which gives rise to a weak–strong uniqueness result (pathwise and in law). A dissipative martingale solution coincides (pathwise or in law) with the strong solution as soon as the latter exists.
Original languageEnglish
Article number80
JournalJournal of Mathematical Fluid Mechanics
Volume23
Issue number3
Early online date15 Jul 2021
DOIs
Publication statusPublished - Aug 2021

Keywords

  • Martingale solutions
  • Stochastic Euler equations
  • Vanishing viscosity
  • Weak–strong uniqueness

ASJC Scopus subject areas

  • Mathematical Physics
  • Condensed Matter Physics
  • Computational Mathematics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Dissipative Solutions to the Stochastic Euler Equations'. Together they form a unique fingerprint.

Cite this