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ERC Workshop on Optimal Transportation and Applications

Topology-preserving Diffusion of Divergence-free Vector Fields

speaker: Yann Brenier (Université Paris-Saclay, Orsay)

abstract: The usual heat equation for divergence-free vector field is not "topology-preserving" because it cannot be written as a transport equation. This is in sharp contrast with the standard scalar heat equation which is easily written as a transport equation (as in JKO theory, for instance). Relying on the concept of optimal transport of strings, we introduce a class of non-linear degenerate diffusion equations that are topology-preserving and have a very large and non-trivial family of equilibrium states, including, in a natural way, many (resp. all) stationary of the 3D (resp. 2D) Euler equations of incompressible fluids.

timetable:
Mon 5 Nov, 9:00 - 9:50, Aula Dini
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