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Existence of distributional solutions to the semigeostrophic equations

Fluid Mechanics, Hamiltonian Dynamics, and Numerical Aspects of Optimal Transportation October 14, 2013 - October 18, 2013

October 14, 2013 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Maria Colombo (Scuola Normale Superiore)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC


Abstract The semigeostrophic equations are a set of equations which model large-scale atmospheric/ocean flows. The system admits a dual version, obtained from the original equations through a change of variable. Existence for the dual problem has been proven in 1998 by Benamou and Brenier, but the existence of a solution of the original system remained open due to the low regularity of the change of variable. In the talk we prove the existence of distributional solutions of the original equations, both in R^3 and in a two-dimensional periodic setting. The proof is based on recent regularity and stability estimates for Alexandrov solutions of the Monge-Amp`ere equation, established by De Philippis and Figalli.
18889?type=thumb Colombo 322 KB application/pdf Download
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