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On a stochastic Leray-\(\alpha\) model of Euler equations. (English) Zbl 1284.35327
Summary: We deal with the 3D inviscid Leray-\(\alpha\) 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 the initial velocity of finite energy and the solution has finite energy a.s. These results continue to hold in the 2D case.

MSC:
35Q31 Euler equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35Q35 PDEs in connection with fluid mechanics
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
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