On the analyticity of the trajectories of the particles in the patch problem for $2$D Euler and aggregation equations
Analysis of PDEs
2020-09-15 v2
Abstract
We give a proof of the analiticity in time for the particle trajectories associated with the solutions of some transport equations when the initial datum is a patch. These results are obtained from a precise study of the Beurling transform, which provides estimates for the solutions of some new equations satisfied by the lagrangian flow.
Keywords
Cite
@article{arxiv.1907.13407,
title = {On the analyticity of the trajectories of the particles in the patch problem for $2$D Euler and aggregation equations},
author = {J. M. Burgués and J. Mateu},
journal= {arXiv preprint arXiv:1907.13407},
year = {2020}
}
Comments
59 pages, 1 figure, revised and clarified some arguments in sections 2 and 3, results unchanged