Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.18105 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913529539330048 |
|---|---|
| author | Giri, Vikram Radu, Razvan-Octavian |
| author_facet | Giri, Vikram Radu, Razvan-Octavian |
| contents | For any $γ<1/3$, we construct a nontrivial weak solution $u$ to the two-dimensional, incompressible Euler equations, which has compact support in time and satisfies $u\in C^γ(\mathbb R_t \times \mathbb T^2_x)$. In particular, the constructed solution does not conserve energy and, thus, settles the flexible part of the Onsager conjecture in two dimensions. The proof involves combining the Nash iteration technique with a new linear Newton iteration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_18105 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Onsager conjecture in 2D: a Newton-Nash iteration Giri, Vikram Radu, Razvan-Octavian Analysis of PDEs For any $γ<1/3$, we construct a nontrivial weak solution $u$ to the two-dimensional, incompressible Euler equations, which has compact support in time and satisfies $u\in C^γ(\mathbb R_t \times \mathbb T^2_x)$. In particular, the constructed solution does not conserve energy and, thus, settles the flexible part of the Onsager conjecture in two dimensions. The proof involves combining the Nash iteration technique with a new linear Newton iteration. |
| title | The Onsager conjecture in 2D: a Newton-Nash iteration |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2305.18105 |