Entropy maximization in the two-dimensional Euler equations
Analysis of PDEs
2026-03-18 v1
Abstract
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.
Cite
@article{arxiv.2405.14738,
title = {Entropy maximization in the two-dimensional Euler equations},
author = {Michele Coti Zelati and Matias G. Delgadino},
journal= {arXiv preprint arXiv:2405.14738},
year = {2026}
}
Comments
29 pages, 1 figure