Analiticity of the Flow for the Aggregation Equation

Abstract

Let $\Omega$ be a bounded domain in ${\mathbb{R}}^n$ whose boundary is $\ka{1,\,γ}$ for $\gamma \in (0,1)$. Consider the aggregation equation in the case of the initial condition being a positive multiple of the characteristic function of $\Omega$. 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.

The abstract rewritten in better English. Argument in the proof of Proposition 1 has been improved. Argument in the proof of Lemma 12 has been clarified. Several typos have been corrected