Local well-posedness of a nonlinear Fokker–Planck model

Abstract

Abstract Noise or fluctuations play an important role in the modeling and understanding of the behavior of various complex systems in nature. Fokker–Planck equations are powerful mathematical tools to study behavior of such systems subjected to fluctuations. In this paper we establish local well-posedness result of a new nonlinear Fokker–Planck equation. Such equations appear in the modeling of the grain boundary dynamics during microstructure evolution in the polycrystalline materials and obey special energy laws.