Abstract:
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].
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Accepted October 9, 2000¶Published online February 14, 2001
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Cullen, M., Gangbo, W. A Variational Approach for the 2-Dimensional Semi-Geostrophic Shallow Water Equations. Arch. Rational Mech. Anal. 156, 241–273 (2001). https://doi.org/10.1007/s002050000124
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DOI: https://doi.org/10.1007/s002050000124