Methods and Applications of Analysis
Volume 27 (2020)
Special Issue for the 60th Birthday of John Urbas: Part I
Guest Editors: Neil Trudinger and Xu-Jia Wang
From Euler to the semi-geostrophic system: convergence under uniform convexity
Pages: 375 – 386
We prove that if the initial data is well prepared, then certain solutions to the Euler system converge to a solution of 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.
SG system, Euler system, flows of maps, optimal mass transport
2010 Mathematics Subject Classification
The work of Mikhail Feldman was supported in part by the National Science Foundation under Grant DMS-1764278, 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.
Received 12 February 2020
Accepted 17 June 2020
Published 24 September 2021