Workshop on Optimal Transportation,
Transport Equations, and Hydrodynamics

11-15 July 2005, Edinburgh

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Yann Brenier (CNRS Nice/Paris VI)
Geoffrey Burton (Bath)

Optimal Transportation theory arose from Monge's mass transfer problem of 1781. Since the 1980s, there has been an upsurge in activity stimulated by the discovery of the monotone rearrangement and polar factorisation of vector valued functions. Through this result, optimal transportation was related to the Monge-Ampere equation, an important nonlinear PDE arising in differential geometry.

Ideas from optimal transport theory are now finding applications in such diverse fields as statistical mechanics, convexity, and integral and geometric inequalities.

Since the first existence theorems for solutions of the Euler equations with discontinuous vorticity were proved in the 1960s, there have been further developments in the realm of weak solutions in hydrodynamics. These developments fit well with the theory of transport by non-smooth vector fields which arose in the 1980s, establishing properties characteristic of the flow of vector field in a context where the trajectories of the flow were not always well-defined, and which are now able to cope with divergence-free BV vector fields.

One of the most exciting models in fluid mechanics, combining both optimal transportation and the theory of transport equations, is the semigeostrophic model of large-scale phenomena in vortex flows.

The workshop seeks to bring together specialists in the three topics of its title, to present the latest developments in each, and to investigate the connections between them.

Numbers of participants are limited. Anyone interested in attending should contact  Geoffrey Burton (grb@maths.bath.ac.uk); the organisers will issue an invitation if space permits.

Created 12 April 2005

This workshop is made possible by grants awarded to ICMS from EPSRC Mathematical Sciences Programme, the Scottish Higher Education Funding Council and the London Mathematical Society.

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