Long-time behaviour and phase transitions for the McKean--Vlasov equation on the torus

J. A. Carrillo, R. S. Gvalani, G. A. Pavliotis +1

We study the McKean-Vlasov equation \[ \partial_t \varrho= β^{-1} Δ\varrho + κ\nabla \cdot (\varrho \nabla (W \star \varrho)) \, , \] with periodic boundary conditions on the torus…