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arXiv · 1911.08974

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

Victor Arnaiz·Ángel Castro
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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.

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Victor Arnaiz, Ángel Castro. 2019-11-20. Singularity formation for the fractional Euler-Alignment system in 1D. https://arxiv.org/abs/1911.08974

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