Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.18509 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916880884695040 |
|---|---|
| author | Giri, Vikram Kwon, Hyunju Novack, Matthew |
| author_facet | Giri, Vikram Kwon, Hyunju Novack, Matthew |
| contents | In this work, we prove the $L^3$-based strong Onsager conjecture for the three-dimensional Euler equations. Our main theorem states that there exist weak solutions which dissipate the total kinetic energy, satisfy the local energy inequality, and belong to $C^0_t (W^{\frac 13-, 3} \cap L^{\infty-})$. More precisely, for every $β<\frac 13$, we can construct such solutions in the space $C^0_t ( B^β_{3,\infty} \cap L^{\frac{1}{1-3β}} )$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_18509 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The $L^3$-based strong Onsager theorem Giri, Vikram Kwon, Hyunju Novack, Matthew Analysis of PDEs 35Q31, 35D30 In this work, we prove the $L^3$-based strong Onsager conjecture for the three-dimensional Euler equations. Our main theorem states that there exist weak solutions which dissipate the total kinetic energy, satisfy the local energy inequality, and belong to $C^0_t (W^{\frac 13-, 3} \cap L^{\infty-})$. More precisely, for every $β<\frac 13$, we can construct such solutions in the space $C^0_t ( B^β_{3,\infty} \cap L^{\frac{1}{1-3β}} )$. |
| title | The $L^3$-based strong Onsager theorem |
| topic | Analysis of PDEs 35Q31, 35D30 |
| url | https://arxiv.org/abs/2305.18509 |