ALEX 2018 Workshop: Abstracts

From initial value problems to some generalized mean field games by convex minimization

Yann Brenier

CNRS, DMA-Ecole Normale Supérieure, Paris (France)

We show that it is possible to solve the initial value problem by a convex optimization problem: i) for short times, in the case of the Euler equations of both incompressible and compressible fluids (and more generally for systems of conservation law admitting a convex entropy), ii) for arbitrarily large time intervals, in the case of Kruzhkov’s entropy solutions to the (non-viscous) Burgers equation. The convex minimization problem is related to the concept of sub-solution in the sense of convex integration theory and can also be interpreted as a kind of generalized variational mean-field game.