Singularity formation for the fractional Euler-Alignment system in 1D

Abstract

We study the formation of singularities for the Euler-Alignment system with influence function $\psi =\frac{k_{\alpha }}{|x{|}^{\alpha }}$ in 1D. As in [20] the problem is reduced to the analysis of a nonlocal 1D equation. We show the existence of singularities in finite time for any $\alpha$ in the range $0<\alpha <2$ in both the real line and the periodic case.

arXiv comment26 pages