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Variational models for incompressible Euler equations

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  • In this paper we illustrate some recent work [1], [2] on Brenier's variational models for incompressible Euler equations. These models give rise to a relaxation of the Arnold distance in the space of measure-preserving maps and, more generally, measure-preserving plans. We analyze the properties of the relaxed distance, we show a close link between the Lagrangian and the Eulerian model, and we derive necessary and sufficient optimality conditions for minimizers. These conditions take into account a modified Lagrangian induced by the pressure field.
    Mathematics Subject Classification: Primary: 49J45; Secondary: 49K99, 76B99.


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