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In the lines of the recent paper [5], we establish various ill-posedness results for the Prandtl equation. By considering perturbations of stationary shear flows, we show that for some linearizations of the Prandtl equation and some C ∞ initial data, local in time C ∞ solutions do not exist. At the nonlinear level, we prove that if a flow exists in the… (More)

This note is devoted to the effect of topography on geophysical flows. We consider two models derived from shallow water theory: the quasigeostrophic equation and the lake equation. Small scale variations of topography appear in these models through a periodic function, of small wavelength ε. The asymptotic limit as ε goes to zero reveals homogenization… (More)

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