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3D Stochastic Primitive Equations of the Large-Scale Ocean: Global Well-Posedness and Attractors

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Abstract

In this paper, we consider the global well-posedness and long-time dynamics for the three-dimensional viscous primitive equations describing the large-scale oceanic motion under a random forcing, which is an additive white in time noise. We firstly prove the existence and uniqueness of global strong solutions to the initial boundary value problem for the stochastic primitive equations. Subsequently, by studying the asymptotic behavior of strong solutions, we obtain the existence of random attractors for the corresponding random dynamical system.

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  1. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, P. R. China

    Boling Guo & Daiwen Huang

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  1. Boling Guo
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  2. Daiwen Huang
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Correspondence to Daiwen Huang.

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Communicated by P. Constantin

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Guo, B., Huang, D. 3D Stochastic Primitive Equations of the Large-Scale Ocean: Global Well-Posedness and Attractors. Commun. Math. Phys. 286, 697–723 (2009). https://doi.org/10.1007/s00220-008-0654-7

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