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.
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: | 21 Nov 2023 08:03 |
| 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