arXiv subjects

J. M. Burgués

Publications and source records attributed to J. M. Burgués.

2 recordsLinked to original sources

arXiv2024

Analiticity of the Flow for the Aggregation Equation

Let $Ω$ be a bounded domain in $\R^n$ whose boundary is $\ka{1,\,γ}$ for $γ\in(0,\,1)$. Consider the aggregation equation in the case of the initial condition being a positive multiple of the characteristic function of $Ω$. In this paper we prove global in time analyticity of the flow generated by the velocity field which propagates the density solution of this equation.

math.AP↗

arXiv2020

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

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.

math.AP↗