The Euler equations in planar nonsmooth convex domains

As a model problem for the barotropic mode of the primitive equations of the oceans and atmosphere, we consider the Euler system on a bounded convex planar domain Ω, endowed with non-penetrating boundary conditions. For 43≤p≤2, and initial and forcing data with Lp(Ω) vorticity we show the existence of a weak solution, enriching and extending the results of Taylor (2000) [32].In the physical case of a rectangular domain Ω=[0, L1]×[0, L2], a similar result holds for all 2<∞ as well. Moreover, by means of a new BMO-type regularity estimate for the Dirichlet problem on a planar domain with corners, we prove uniqueness of solutions with bounded initial vorticity. © 2013 Elsevier Ltd.