Viorel Barbu
Octav Mayer Institute of Mathematics, Romanian Academy, Iaşi

This talk is concerned with the existence theory for the Fokker-Planck equations (NFPEs) $$\small{ \begin{array} \ u_t-\displaystyle\sum^d_{i,j=1}D^2_{ij}(a_{ij}(x,u)u)+{\rm div}(b(x,u)u)=0\mbox{ in }(0,\infty)\times\mathbb{R}^d\!, \\ u(0,x)=u_0(x),\ x\in\mathbb{R}^d. \end{array}}$$ This equation is relevant in statistical mechanics, mean field theory and also in stochastic analysis. In fact, a distributional solution $u$ of this equation describes the microscopic dynamics of the stochastic differential differential equation (McKean-Vlasov SDE) $$dX=b(x,u)dt+\sigma(x,u)dW.$$ The results are surveyed here were obtained in collaboration with Michael Röckner (Bielefeld University).