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arXiv · 1111.1451

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

Nathan E. Glatt-Holtz·Vlad C. Vicol
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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 very general nonlinear multiplicative noise. In the two-dimensional case we obtain the global existence of these solutions with additive or linear-multiplicative noise. Lastly, 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. 2011-11-06. Local and global existence of smooth solutions for the stochastic Euler equations with multiplicative noise. https://arxiv.org/abs/1111.1451

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