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Classical Solutions to Semi-geostrophic System with Variable Coriolis Parameter

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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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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin, Madison, WI, 53706, USA

    Jingrui Cheng & Mikhail Feldman

  2. Met Office, Fitzroy Road, Exeter, Devon, EX1 3PB, UK

    Michael Cullen

Authors
  1. Jingrui Cheng
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  2. Michael Cullen
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  3. Mikhail Feldman
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Correspondence to Mikhail Feldman.

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Communicated by A. Figalli

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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

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