Then initial value problem for the Euler equations of fluids viewed as a convex optimisation problem

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• Yann Brenier, CNRS & Ecole Normale Supérieure, Paris
• Monday 21 May 2018, 15:00-16:00
• CMS, MR13.

If you have a question about this talk, please contact Ivan Moyano.

We consider the initial value problem for the Euler equations of inviscid fluids and, more generally, for “conservation laws with convex entropy”. It is shown that any smooth solution to the initial value problem, at least for short time, can be recovered by solving a suitable convex optimisation problem. This problem, which can be solved for arbitrarily long time intervals, makes bridges between the three theories of optimal transport, mean field game and convex integration. In the elementary case of the “inviscid” Burgers equation, it is shown that every entropy solution, including shocks, can be recovered without any restriction on the time interval.

This talk is part of the Partial Differential Equations seminar series.

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