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Bulletin of the American Mathematical Society

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High dimensionality and h-principle in PDE


Authors: Camillo De Lellis and László Székelyhidi Jr.
Journal: Bull. Amer. Math. Soc. 54 (2017), 247-282
MSC (2010): Primary 35Q31; Secondary 35A01, 35D30, 76F02, 53A99, 53C21
DOI: https://doi.org/10.1090/bull/1549
Published electronically: October 20, 2016
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Camillo De Lellis
Affiliation: Institut für Mathematik, Universität Zürich, CH-8057 Zürich
Email: camillo.delellis@math.uzh.ch

László Székelyhidi Jr.
Affiliation: Mathematisches Institut, Universität Leipzig, D-04009 Leipzig
Email: laszlo.szekelyhidi@math.uni-leipzig.de

DOI: https://doi.org/10.1090/bull/1549
Received by editor(s): July 11, 2016
Published electronically: October 20, 2016
Additional Notes: The research of the first author has been supported by the grant $200021_159403$ of the Swiss National Foundation.
The second author gratefully acknowledges the support of ERC Grant Agreement No. 277993
Article copyright: © Copyright 2016 American Mathematical Society