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January 2014 Local and global existence of smooth solutions for the stochastic Euler equations with multiplicative noise
Nathan E. Glatt-Holtz, Vlad C. Vicol
Ann. Probab. 42(1): 80-145 (January 2014). DOI: 10.1214/12-AOP773

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 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.

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Nathan E. Glatt-Holtz. Vlad C. Vicol. "Local and global existence of smooth solutions for the stochastic Euler equations with multiplicative noise." Ann. Probab. 42 (1) 80 - 145, January 2014. https://doi.org/10.1214/12-AOP773

Information

Published: January 2014
First available in Project Euclid: 9 January 2014

zbMATH: 1304.35545
MathSciNet: MR3161482
Digital Object Identifier: 10.1214/12-AOP773

Subjects:
Primary: 35Q35, 60H15
Secondary: 76B03

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 1 • January 2014
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