A variational approach for the 2-D semi-geostrophic shallow water equations
نویسندگان
چکیده
Existence of weak solutions to the 3-D semi-geostrophic equations with rigid boundaries was proved by Benamou and Brenier [3], using Monge transport theory. This paper extends the results to a free surface boundary condition, which is more physically appropriate. This extension is at present for the 2-D shallow water case only. In addition, we establish stronger time regularity than was possible in [3]. ∗WG gratefully acknowledges the support of National Science Foundation grants DMS 96-22734 and DMS-99-70520.
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