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Exponential stability of the quasigeostrophic equation under random perturbations. (English) Zbl 0987.76027

Imkeller, Peter (ed.) et al., Stochastic climate models. Proceedings of a workshop, Chorin, Germany, Summer 1999. Basel: Birkhäuser. Prog. Probab. 49, 241-256 (2001).
The quasigeostrophic equation is a simplified geophysical fluid model, derived as an approximation of rotating shallow water equations for small Rossby numbers or for high rotation rates. Here, the authors investgate the barotropic quasigeostrophic equation which is the lowest-order approximation. This equation is considered under random forcing induced additively by a trace-class Wiener process, and with random boundary conditions into which enters another trace-class Wiener process. It is shown that, for sufficiently small noise and small Coriolis parameter, and for sufficiently high viscosity and Ekman number, there exists a unique stationary solution, and every other solution converges exponentially fast to this stationary solution.
For the entire collection see [Zbl 0961.00022].

MSC:

76E20 Stability and instability of geophysical and astrophysical flows
76U05 General theory of rotating fluids
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
76M35 Stochastic analysis applied to problems in fluid mechanics
86A05 Hydrology, hydrography, oceanography
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