Exponential stability of the quasigeostrophic equation under random perturbations

Duan, Jinqiao; Kloeden, Peter E.; Schmalfuß, Björn

doi:10.1007/978-3-0348-8287-3_10

Cited by 10 publications

(13 citation statements)

References 20 publications

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“…There is recent work on random dynamical attractors for the quasigeostrophic flow model by Duan et al [6]. A consequence of that work implies that, when viscosity is sufficiently large and when the trace of the covariance operator for the Wiener process is sufficiently small, then all quasigeostrophic motions approach a point random attractor exponentially fast as time goes to infinity.…”

Section: Discussionmentioning

confidence: 99%

Ergodicity of stochastically forced large scale geophysical flows

Duan

Gołdys

2001

International Journal of Mathematics and Mathematical Sciences

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Abstract. We investigate the ergodicity of 2D large scale quasigeostrophic flows under random wind forcing. We show that the quasigeostrophic flows are ergodic under suitable conditions on the random forcing and on the fluid domain, and under no restrictions on viscosity, Ekman constant or Coriolis parameter. When these conditions are satisfied, then for any observable of the quasigeostrophic flows, its time average approximates the statistical ensemble average, as long as the time interval is sufficiently long.2000 Mathematics Subject Classification. 37A25, 60H15, 76D05, 86A05.

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Section: Discussionmentioning

confidence: 99%

Ergodicity of stochastically forced large scale geophysical flows

Duan

Gołdys

2001

International Journal of Mathematics and Mathematical Sciences

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“…With this alternative viewpoint, Markov chains in random environments arise in analyses of time-dependent dynamical systems, such as models of stirred fluids [13] and circulation models of the ocean and atmosphere [8,2,4]. In these settings, one can convert the typically low-dimensional nonlinear dynamics into infinite-dimensional linear dynamics by studying the dynamical action on functions on the low-dimensional space, (representing densities of invariant measures with respect to a suitable reference measure).…”

Section: Alternative Viewpoint Of the Random Environment And Applicatmentioning

confidence: 99%

Stability and approximation of invariant measures of Markov chains in random environments

Froyland

González-Tokman

2015

Stoch. Dyn.

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We consider finite-state Markov chains driven by stationary ergodic invertible processes representing random environments. Our main result is that the invariant measures of Markov chains in random environments (MCREs) are stable under a wide variety of perturbations. We prove stability in the sense of convergence in probability of the invariant measure of the perturbed MCRE to the original invariant measure. We also develop a new numerical scheme to construct rigorous approximations of the invariant measures, which converge in probability as the resolution of the scheme increases. This numerical approach is illustrated with an example of a random walk in a random environment.

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“…There are many works about mathematical study of some stochastic climate models, see, e.g., [6][7][8]19,20]. Ref.…”

Section: Introductionmentioning

confidence: 99%

Diffusion limit of 3D primitive equations of the large-scale ocean under fast oscillating random force

Guo

Huang

Wang

2015

Journal of Differential Equations

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The three-dimensional (3D) viscous primitive equations describing the large-scale oceanic motions under fast oscillating random perturbation are studied. Under some assumptions on the random force, the solution to the initial boundary value problem (IBVP) of the 3D random primitive equations converges in distribution to that of IBVP of the limiting equations, which are the 3D stochastic primitive equations describing the large-scale oceanic motions under a white in time noise forcing. This also implies the convergence of the stationary solution of the 3D random primitive equations.

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Exponential stability of the quasigeostrophic equation under random perturbations

Cited by 10 publications

References 20 publications

Ergodicity of stochastically forced large scale geophysical flows

Ergodicity of stochastically forced large scale geophysical flows

Stability and approximation of invariant measures of Markov chains in random environments

Diffusion limit of 3D primitive equations of the large-scale ocean under fast oscillating random force

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