The Global Attractor Associated with the Viscous Lake Equations
نویسنده
چکیده
We consider the motion of an incompressible fluid confined to a shallow basin with varying bottom topography. A two-dimensional shallow water model has been derived from a three-dimensional anisotropic eddy viscosity model and has been shown to be globally well posed in [15]. The dynamical system associated with the shallow water model is studied. We show that this system possesses a global attractor and that the Hausdorff and box-counting dimensions of this attractor are bounded above by a value proportional to the weighted L2-norm of the wind forcing function. A weighted Sobolev-Lieb-Thirring inequality plays the key role in the obtention of the dimension estimate.
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