Entropy maximization in the two-dimensional Euler equations
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914400425738240 |
|---|---|
| author | Zelati, Michele Coti Delgadino, Matias G. |
| author_facet | Zelati, Michele Coti Delgadino, Matias G. |
| contents | We consider variational problem related to entropy maximization in the two-dimensional Euler equations, in order to investigate the long-time dynamics of solutions with bounded vorticity. Using variations on the classical min-max principle and borrowing ideas from optimal transportation and quantitative rearrangement inequalities, we prove results on the structure of entropy maximizers arising in the investigation of the long-time behavior of vortex patches. We further show that the same techniques apply in the study of stability of the canonical Gibbs measure associated to a system of point vortices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14738 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entropy maximization in the two-dimensional Euler equations Zelati, Michele Coti Delgadino, Matias G. Analysis of PDEs We consider variational problem related to entropy maximization in the two-dimensional Euler equations, in order to investigate the long-time dynamics of solutions with bounded vorticity. Using variations on the classical min-max principle and borrowing ideas from optimal transportation and quantitative rearrangement inequalities, we prove results on the structure of entropy maximizers arising in the investigation of the long-time behavior of vortex patches. We further show that the same techniques apply in the study of stability of the canonical Gibbs measure associated to a system of point vortices. |
| title | Entropy maximization in the two-dimensional Euler equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.14738 |