High dimensionality and h-principle in PDE

De Lellis, Camillo; Székelyhidi, László, Jr.

doi:10.1090/bull/1549

High dimensionality and h-principle in PDE
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by Camillo De Lellis and László Székelyhidi Jr. PDF

Bull. Amer. Math. Soc. 54 (2017), 247-282 Request permission

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.

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