The initial value problem for the Euler equations of incompressible fluids viewed as a concave maximization problem

Yann Brenier

doi:10.1007/s00220-018-3240-7

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arXiv · 1706.04180

The initial value problem for the Euler equations of incompressible fluids viewed as a concave maximization problem

Yann Brenier

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Abstract

We consider the Euler equations of incompressible fluids and attempt to solve the initial value problem with the help of a concave maximization problem.We show that this problem, which shares a similar structure with the optimal transport problemwith quadratic cost, in its "Benamou-Brenier" formulation,always admits a relaxed solution that can be interpretedin terms of $sub-solution$ of the Euler equations in the sense of convex integration theory.Moreover, any smooth solution of the Euler equations can be recovered from this maximization problem, at least for short times.

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Yann Brenier. 2017-06-12. The initial value problem for the Euler equations of incompressible fluids viewed as a concave maximization problem. https://doi.org/10.1007/s00220-018-3240-7

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