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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.
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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > General Mathematics
Physical Sciences > Applied Mathematics |
| Language: | English |
| Date: | 2017 |
| Deposited On: | 19 Jan 2018 11:43 |
| Last Modified: | 16 Sep 2024 01:37 |
| Publisher: | American Mathematical Society |
| ISSN: | 0273-0979 |
| Funders: | Schweizerischer Nationalfonds |
| OA Status: | Green |
| Free access at: | Publisher DOI. An embargo period may apply. |
| Publisher DOI: | https://doi.org/10.1090/bull/1549 |
De Lellis, Camillo