The Non-Linear Fokker–Planck Equation in Low-Regularity Space

Abstract

We construct the global existence and exponential time decay rates of mild solutions to the non-linear Fokker–Planck equation near a global Maxwellians with small-amplitude initial data in the low regularity function space Lk1LT∞Lv2 where the regularity assumption on the initial data is weaker.

Keywords

• non-linear Fokker–Planck equation
• global existence
• exponential time decay rates
• low regularity function space