Convergence to equilibrium for a degenerate McKean–Vlasov equation

In this work we study the convergence to equilibrium for a (potentially) degenerate nonlinear and nonlocal McKean–Vlasov equation. We show that the solution to this equation is related to the solution of a linear degenerate and/or defective Fokker–Planck equation and employ recent sharp convergence results to obtain an easily computable (and many times sharp) rates of convergence to equilibrium for the equation in question.