Flow selections for (nonlinear) Fokker–Planck–Kolmogorov equations

We provide a method to select flows of solutions the Cauchy problem for linear and nonlinear Fokker–Planck–Kolmogorov equations (FPK equations) measures on Euclidean space. In case, our improves similar results previous work author. Our consideration flow selections equations, including particularly interesting case Nemytskii-type coefficients, seems be new. also characterize (restricted) well-posedness FPK by uniqueness such flows. Moreover, we show that under suitable assumptions in are Markovian, i.e. they fulfill Chapman-Kolmogorov equations.