Title: Global regularity for 1D Eulerian dynamics with singular interaction forces,
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.