| In this dissertation,we study the well-posedness of kinetic Mean-field SDEs with singular environmental noise.To this end,we investigate singular kinetic equations on R2dby the paracontrolled distribution method introduced in[46].We develop paracon-trolled calculus in the kinetic setting,and use it to establish the global well-posedness for the linear singular kinetic equations.We also demonstrate how the required products of Gaussian random field can be renormalized by probabilistic calculation.Interest-ingly,although the terms in the zeroth Wiener chaos of regularization approximation are not zero,they converge in suitable weighted Besov spaces and no renormalization is required.As a result we obtain the well-posedness of nonlinear martingale problem for kinetic Mean-field SDEs with singular drifts.Moreover,the global well-posedness for a nonlinear kinetic Fokker-Planck equation with singular coefficients is obtained by the entropy method. |
