The Annals of Probability
- Ann. Probab.
- Volume 42, Number 1 (2014), 80-145.
Local and global existence of smooth solutions for the stochastic Euler equations with multiplicative noise
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 two-dimensional case we obtain the global existence of these solutions with additive or linear-multiplicative noise. Finally, we show that, in the three-dimensional 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.
Ann. Probab., Volume 42, Number 1 (2014), 80-145.
First available in Project Euclid: 9 January 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35Q35: PDEs in connection with fluid mechanics 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 76B03: Existence, uniqueness, and regularity theory [See also 35Q35]
Glatt-Holtz, Nathan E.; Vicol, Vlad C. Local and global existence of smooth solutions for the stochastic Euler equations with multiplicative noise. Ann. Probab. 42 (2014), no. 1, 80--145. doi:10.1214/12-AOP773. https://projecteuclid.org/euclid.aop/1389278521