On the analyticity of the trajectories of the particles in the patch problem for D Euler and aggregation equations
arXiv:1907.13407
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.
arXiv comment59 pages, 1 figure, revised and clarified some arguments in sections 2 and 3, results unchanged