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One proves in this work that the nonlinear semigroup $S(t)$ in $L^1(\mathbbR^d)$, $d\geq 3$, associated with the nonlinear Fokker-Planck equation$u_t-\Delta\beta(u)+\text{div}(Db(u)u){=}0$, $u(0)=u_0$ in$(0,\infty)\times\mathbb R^d$, under suitable conditions on the coefficients$\beta:\mathbb R\to\mathbb R$, $D:\mathbb R^d\to\mathbb R^d$ and $b:\mathbbR\to\mathbb R$, is mean ergodic. In particular, this implies the meanergodicity of the time marginal laws of the solutions to the correspondingMcKean-Vlasov stochastic differential equation. This completes the resultsestablished in [7] on the nature of the corresponding omega-set $\omega(u_0)$for $S(t)$ in the case where the flow $S(t)$ in $L^1(\mathbb R^d)$ has not afixed point and so the corresponding stationary Fokker-Planck equation has nosolutions.

The ergodicity of nonlinear Fokker-Planck flows in $L^1(\mathbb R^d)$