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arXiv · 1907.13407

On the analyticity of the trajectories of the particles in the patch problem for $2$D Euler and aggregation equations

J. M. Burgués·J. Mateu
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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.

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J. M. Burgués, J. Mateu. 2019-07-31. On the analyticity of the trajectories of the particles in the patch problem for $2$D Euler and aggregation equations. https://arxiv.org/abs/1907.13407

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