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On the primitive equations of large-scale ocean with random boundary. (English) Zbl 1240.86003

Summary: This paper is concerned with global well-posedness and the existence of attractors for the three-dimensional viscous primitive equations, describing large-scale oceanic motion under random wind stress. We prove global well-posedness of the primitive equations with white-noise boundary conditions. Moreover, by studying the asymptotic behavior of strong solutions, we obtain the existence of random attractors for the corresponding random dynamical system.

MSC:

86A05 Hydrology, hydrography, oceanography
35Q35 PDEs in connection with fluid mechanics
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
76D05 Navier-Stokes equations for incompressible viscous fluids
76M35 Stochastic analysis applied to problems in fluid mechanics
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