On a Stochastic Leray-α model of Euler equations

Abstract

We deal with the 3D inviscid Leray-α model. The well posedness for this problem is not known; by adding a random perturbation we prove that there exists a unique (in law) global solution. The random forcing term formally preserves conservation of energy. The result holds for initial velocity of finite energy and the solution has finite energy a.s.. These results are easily extended to the 2D case.

25 pages; a reference updated;few comments added

References in corpus (2)

• Well-posedness of the transport equation by stochastic perturbation
• Anomalous dissipation in a stochastic inviscid dyadic model

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