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

Bessaih, Hakima

Electron. J. Probab. 5, Paper No. 3, 16 p. (2000).

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

Keywords:

dissipative Euler equation; random dynamical systems; attractors