文献类型：期刊文献

中文题名：The Hydrodynamic Limit of Nonlinear Fokker-Planck Equation

英文题名：The Hydrodynamic Limit of Nonlinear Fokker-Planck Equation

作者：Yi’ang Ren[1];Lijuan Yu[1];Jie Liao[1]

机构：[1]Department of Mathematics, East China University of Science and Technology, Shanghai, China

年份：2020

卷号：8

期号：11

起止页码：2488

中文期刊名：Journal of Applied Mathematics and Physics

外文期刊名：应用数学与应用物理（英文）

语种：英文

中文关键词：Non-Linear Fokker-Planck Equation;Macro-Micro Decomposition;Fluid-Type System;Viscosity;Heat Diffusion

外文关键词：Non-Linear Fokker-Planck Equation;Macro-Micro Decomposition;Fluid-Type System;Viscosity;Heat Diffusion

摘要：The non-linear Fokker-Planck equation arises in describing the evolution of stochastic system, which is a variant of the Boltzmann equation modeling the evolution of the random system with Brownian motion, where the collision term is replaced by a drift-diffusion operator. This model conserves mass, momentum and energy;the dissipation is much weaker than that in a simplified model we considered before which conserved only mass, thus more difficult to analyze. The macro-micro decomposition of the solution around the local Maxwellian introduced by T.-P. Liu, T. Yang and S.-H. Yu for Boltzmann equation is used, to reformulate the model into a fluid-type system incorporate viscosity and heat diffusion terms, coupled with an equation of the microscopic part. The viscosity and heat diffusion terms can give dissipative mechanism for the analysis of the model.
The non-linear Fokker-Planck equation arises in describing the evolution of stochastic system, which is a variant of the Boltzmann equation modeling the evolution of the random system with Brownian motion, where the collision term is replaced by a drift-diffusion operator. This model conserves mass, momentum and energy;the dissipation is much weaker than that in a simplified model we considered before which conserved only mass, thus more difficult to analyze. The macro-micro decomposition of the solution around the local Maxwellian introduced by T.-P. Liu, T. Yang and S.-H. Yu for Boltzmann equation is used, to reformulate the model into a fluid-type system incorporate viscosity and heat diffusion terms, coupled with an equation of the microscopic part. The viscosity and heat diffusion terms can give dissipative mechanism for the analysis of the model.