Global solutions to a nonlinear Fokker-Planck equation

Abstract

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_{x}L^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, J. Stat. Phys., 173 (2018), 222–241.), the regularity assumption on the initial data is much weaker.

Keywords

• nonlinear fokker-planck equation
• global existence
• energy method
• cauchy problem
• priori estimates