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Global well-posedness and finite-dimensional global attractor for a 3-D planetary geostrophic viscous model. (English) Zbl 1035.37043
The authors study a three-dimensional planetary geostrophic viscous model of the gyre-scale mid-latitude ocean, with wind-driven boundary conditions on the top surface and nonslip, no-flux conditions on the side walls and bottom. The main results are the existence and uniqueness of global weak and strong solutions, the existence of a global attractor, as well as an upper bound estimate of its dimension.
MSC:
37N10Dynamical systems in fluid mechanics, oceanography and meteorology
37L30Attractors and their dimensions, Lyapunov exponents
35Q35PDEs in connection with fluid mechanics
76D99Incompressible viscous fluids
86A05Hydrology, hydrography, oceanography
35B41Attractors (PDE)