35 Partial differential equations -- 35Q Equations of mathematical physics and other areas of application 35Q82 PDEs in connection with statistical mechanics
Summary: ``In this paper, we construct global solutions to the Cauchy problem on a nonlinear Fokker-Planck equation near Maxwellian with small-amplitude initial data in Sobolev space $H^2_xL^2_v$ by a refined nonlinear energy method. Compared with the results of Liao et al. (Global existence and decay rates of the solutions near Maxwellian for non-linear Fokker-Planck equations, {\it J. Stat. Phys.}, {\bf 173} (2018), 222--241.) [MR3859533], the regularity assumption on the initial data is much weaker.''