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Free upper boundary value problems for the semi-geostrophic equations

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

October 16, 2013 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Michael Cullen (Met Office)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC

Abstract I consider the flow of three-dimensional stratified rotating fluid with a free upper boundary. I show how the semi-geostrophic equations are derived as a limit of the Euler equations. Following earlier work of Benamou and Brnier, and Cullen and Gangbo, the equations are formulated in dual variables and the mapping to physical space is determined by optimal transportation using the energy as the cost function. I focus on the differences from the earlier work. These are the form of the energy, the definition of the space in which the energy is to be minimised, and the proof that the energy is strictly convex with respect to variations in the free upper boundary
18899?type=thumb Cullen 559 KB application/pdf Download
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