Abstract
We prove a weak-strong uniqueness result for the semi-geostrophic system with constant Coriolis force. The main assumptions on the strong solution are the boundedness of the velocity field as well as the uniform convexity of the Legendre-Fenchel transform of the modified pressure. We give several examples where our results apply, including some classical solutions on the 2-dimensional torus, and the “stationary” solutions for 3DSG (for which the total wind velocity is zero but the pressure may be time-dependent).
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Acknowledgements
The work of Mikhail Feldman was supported in part by the National Science Foundation under Grant DMS-1401490, and the Van Vleck Professorship Research Award by the University of Wisconsin-Madison. Adrian Tudorascu was partially supported by the National Science Foundation under Grant DMS-1600272 and by Grant #246063 from the Simons Foundation.
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Communicated by L. Ambrosio.
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Feldman, M., Tudorascu, A. The semi-geostrophic system: weak-strong uniqueness under uniform convexity. Calc. Var. 56, 158 (2017). https://doi.org/10.1007/s00526-017-1254-1
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DOI: https://doi.org/10.1007/s00526-017-1254-1