High dimensionality and H-principle in PDE

Abstract

In this note we present "an analyst's point of view" on the Nash- Kuiper Theorem and, in particular, highlight the very close connection to turbulence-a paradigm example of a high-dimensional phenomenon. Our aim is to explain recent applications of Nash's ideas in connection with the incompressible Euler equations and Onsager's famous conjecture on the energy dissipation in 3D turbulence.