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High dimensionality and h-principle in PDE


De Lellis, Camillo; Székelyhidi, László (2017). High dimensionality and h-principle in PDE. Bulletin (new series) of the American Mathematical Society, 54(2):247-282.

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.

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 indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2017
Deposited On:19 Jan 2018 11:43
Last Modified:18 Apr 2018 11:48
Publisher:American Mathematical Society
ISSN:0273-0979
Funders:Schweizerischer Nationalfonds
OA Status:Hybrid
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1090/bull/1549

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