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

Global regularity for 1D Eulerian dynamics with singular interaction forces