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 language | English (US) |
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Pages (from-to) | 80-145 |
Number of pages | 66 |
Journal | Annals of Probability |
Volume | 42 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2014 |
Keywords
- Compactness methods
- Euler equations
- Nonlinear multiplicative noise
- Pathwise solutions
- Stochastic partial differential equations on lebesgue spaces
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty