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 ΩΩ, endowed with non-penetrating boundary conditions. For 43≤p≤2, and initial and forcing data with Lp(Ω)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]Ω=[0,L1]×[0,L2], a similar result holds for all 2