The h-principle in fluid mechanics

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• Laszlo Szekelyhidi (Leipzig)
• Wednesday 26 October 2016, 13:00-14:00
• CMS, MR12.

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It is known since the pioneering work of Scheffer and Shnirelman that weak solutions of the incompressible Euler equations exhibit a wild behaviour, which is very different from that of classical solutions. Nevertheless, weak solutions in three space dimensions have been studied in connection with a long-standing conjecture of Lars Onsager from 1949 concerning anomalous dissipation and, more generally, because of their possible relevance to the K41 theory of turbulence.

In joint work with Camillo De Lellis we established a connection between the theory of weak solutions of the Euler equations and the Nash-Kuiper theorem on rough isometric immersions. Through this connection one can interpret the wild behaviour of weak solutions of Euler as an instance of Gromov’s h-principle. In this lecture I will explain this connection and outline recent progress concerning Onsager’s conjecture.

This talk is part of the Special DPMMS Colloquium series.

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