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Stochastic weak attractor for a dissipative Euler equation. (English) Zbl 0941.35073

Summary: A nonautonomous dynamical system is considered, a stochastic one that is obtained from the dissipative Euler equation subject to a stochastic perturbation an additive noise. Absorbing sets are defined as sets that depend on time and attract from \(-\infty\). A stochastic weak attractor is constructed in phase space with respect to two metrics and is shown to be compact in the lower one.

MSC:

35Q35 PDEs in connection with fluid mechanics
37L55 Infinite-dimensional random dynamical systems; stochastic equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
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