Global regularity for 1D eulerian dynamics with singular interaction forces
© 2018 Society for Industrial and Applied Mathematics. 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 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 [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.
Volume / Issue
Start / End Page
Electronic International Standard Serial Number (EISSN)
International Standard Serial Number (ISSN)
Digital Object Identifier (DOI)