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Monday, 24 July 2017 23:04

Global regularity for 1D Eulerian dynamics with singular interaction forces

 

Alexander Kiselev, and Changhui Tan

SIAM Journal on Mathematical Analysis, Volume 50, No 6, pp. 6208–6229 (2018).


Abstract

The Euler–Poisson-alignment (EPA) system appears in mathematical biology and is used to model, in a hydrodynamic limit, a set of agents interacting through mutual attrac- tion/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 [Do et al., Arch. Ration. Mech. Anal., 228 (2018), pp. 1–37]. 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.


   doi:10.1137/17M1141515
 Download the Published Version
 This work is supported by NSF grant DMS #1853001
Read 28973 times Last modified on Monday, 19 July 2021 01:12