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.


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