Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591724 | Journal of Functional Analysis | 2009 | 28 Pages |
Abstract
We establish the existence of a local smooth solution of the stochastic Euler equations in R3. Probabilistic estimate of the random time interval for the existence of a local solution is expressed in terms of expected values of the initial data and the random noise. There are numerous works on the stochastic Euler equations in a two-dimensional domain. Even for the deterministic Euler equations in a three-dimensional domain, the only results are concerned with the local existence of smooth solutions. Our goal is to extend such local existence result to the stochastic equations.
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