Global existence of solutions to some equations modeling phase separation of self-propelled particles

Abstract

In this paper, we provide mathematical results on some models of phase separation of self-propelled particles. To this end, we first introduce a general model presented in Tiribocchi et al. (Phys Rev Lett 115:188302, 2015). We then proceed to handle some particular cases where λ, whose role is to violate time reversal symmetry, is zero (passive) or nonzero (active). We also cover some models coupled with incompressible fluids.