High dimensionality and h-principle in PDE
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- by Camillo De Lellis and László Székelyhidi Jr. PDF
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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.References
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Additional Information
- Camillo De Lellis
- Affiliation: Institut für Mathematik, Universität Zürich, CH-8057 Zürich
- MR Author ID: 657273
- ORCID: 0000-0002-4089-7129
- Email: camillo.delellis@math.uzh.ch
- László Székelyhidi Jr.
- Affiliation: Mathematisches Institut, Universität Leipzig, D-04009 Leipzig
- MR Author ID: 733106
- Email: laszlo.szekelyhidi@math.uni-leipzig.de
- 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 - © Copyright 2016 American Mathematical Society
- 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
- MathSciNet review: 3619726