Singularity formation for the fractional Euler-alignment system in 1D.

We study the formation of singularities for the Euler-alignment system with influence function ψ = kα / |x|1+α in 1D. As in [Commun. Math. Sci. 17 (2019), pp. 1779-1794] the problem is reduced to the analysis of a nonlocal 1D equation. We show the existence of singularities in finite time for any α in the range 0 < α < 2 in both the real line and the periodic case and with just a point of vacuum. [ABSTRACT FROM AUTHOR]