Perlen-Kolloquium: Prof. Dr. Emil Wiedemann (Universität Ulm)

Convex Integration in a Nutshell

Convex integration is a technique, or rather a broad range of techniques, that originated in Nash's work on isometric embeddings of manifolds in the 1950s. It serves to produce 'unexpected' solutions to various geometric or analytic problems with peculiar behaviour. Convex integration has become very trendy again in the past ten years or so, when it turned out that it surprisingly applies to the fundamental equations of fluid mechanics, including the Euler and Navier-Stokes systems. Since contemporary applications, however, have become increasingly technical, it is often not easy to grasp the fundamental mechanism. I will attempt to present this convex integration mechanism in a simple way, and to discuss some applications to isometric embedding, fluid dynamics, and breakdown of the chain rule for functions of low regularity.

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