We consider the surface quasi-geostrophic equation with
critical dissipation and dispersive forcing set on the vertical strip $\Omega=
[-1, 1] \times \mathbb{R}^2 $, with homogeneous Dirichlet boundary conditions for the surface temperature. Similar models for the quasi-geostrophic ocean circulation model of potential vorticity have been treated, where the presence of horizontal boundary layers serves to represent the western intensification of boundary currents.
Our aim is to display this phenomenon by constructing a boundary layer approximation which converges to the global weak solutions of the system, in the limit of large dispersive forcing. We adapt the Strichartz estimates from the full space to the strip and use the dispersive effects to control the nonlinearity. As in the case of the full space this also allows us to show that the asymptotic behavior of solutions is determined by the linear part of the system, that is, we obtain the stabilization effect by Rossby wave propagation. The convergence of the approximations is shown in the energy norm.
Work with Gabriela Planas (Unicamp, Campinas, Brazil)
