Global regularity for 1D Eulerian dynamics with singular interaction forces

2017/07/23 by Alexander Kiselev, Kiselev, Alexander, Changhui Tan +1 · 2 citations
Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1707.07296

openalex publication_date 2017/07/23 · openalex created_date 2017/07/31 · openalex updated_date 2026/07/28

Abstract

The Euler-Poisson-Alignment (EPA) system appears in mathematical biology and is used to model, in a hydrodynamic limit, a set agents interacting through mutual attraction/repulsion as well as alignment forces. We consider one-dimensional EPA system with a class of singular alignment terms as well as natural attraction/repulsion terms. The singularity of the alignment kernel produces an interesting effect regularizing the solutions of the equation and leading to global regularity for wide range of initial data. This was recently observed in the paper by Do, Kiselev, Ryzhik and Tan. Our goal in this paper is to generalize the result and to incorporate the attractive/repulsive potential. We prove that global regularity persists for these more general models.

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• Exponential and algebraic decay in Euler--alignment system with nonlocal interaction forces
• A nonlocal Aw-Rascle-Zhang system with linear pressure term

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