Abstract
We prove the short time existence and uniqueness of smooth solutions (in \({C^{k+2,\alpha}}\) with \({k \geqq 2}\)) to the 2-D semi-geostrophic system and the semi-geostrophic shallow water system with variable Coriolis parameter f and periodic boundary conditions, under the natural convexity condition on the initial data. The dual space used in analysis of the semi-geostrophic system with constant f is not available for the variable Coriolis parameter case, and we develop a time-stepping procedure in Lagrangian coordinates in the physical space to overcome this difficulty.
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Cheng, J., Cullen, M. & Feldman, M. Classical Solutions to Semi-geostrophic System with Variable Coriolis Parameter. Arch Rational Mech Anal 227, 215–272 (2018). https://doi.org/10.1007/s00205-017-1159-3
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DOI: https://doi.org/10.1007/s00205-017-1159-3