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Jan 12
3:30 PM - 4:30 PM KAP 414
Local and global existence of smooth solutions for the stochastic Euler equations on a bounded domain
Nathan Glatt-Holtz Indiana University

We prove the local existence of pathwise solutions for the stochastic Euler equa tions in a three-dimensional bounded domain, with a general nonlinear multiplica tive noise and slip boundary conditions. In the two-dimensional case, we obtain the global existence of these solutions with additive or linear-multiplicative n oise. Lastly, we show that linear multiplicative noise provides a regularizing effect in the sense that the global existence of solutions occurs with high prob ability if the initial data is sufficiently small or if the noise coefficient is sufficiently large. This is recent joint work with V. Vicol.

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