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The h-principle for the Euler equations

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If you have a question about this talk, please contact Jonathan Ben-Artzi.

In a joint work with Laszlo Szekelyhidi we construct continuous weak solutions of the 3d incompressible Euler equations, which dissipate the total kinetic energy. The construction is based on the scheme introduced by J. Nash for producing C1 isometric embeddings, which was later developed by M.Gromov into what became known as convex integration. Weak versions of convex integration (e.g. based on the Baire category theorem) have been used previously to construct bounded (but highly discontinuous) weak solutions. The current construction is the first instance of Nash’s scheme being applied to a PDE which one might classify as “hard” as opposed to “soft”.

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

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