空间齐次的Fokker-Planck-Boltzmann方程

The Spatially Homogeneous Fokker-Planck-Boltzmann Equation

本文讨论如下空间齐次的Fokker Planck Boltzmann方程 : f t-νΔξf=Q(f,f) ,f( ξ ,0 ) =f0 ( ξ) ,这里Q(f,f)是Boltzmann碰撞算子 .在角截断的硬位势情况下 ,我们利用算子半群理论和紧性方法证明了当初始值属于L12 时该方程古典解的整体存在性 ,并且建立了能量线性增长关系式 .

In this paper,we discuss the following spatially homogeneous Fokker-Planck-Boltzmann equation:ft-ν Δ ξf=Q(f,f),f(ξ,0)=f 0(ξ),where Q(f,f) is the Boltzmann collision operator.In the case of hard potentials with angular cut-off,we prove,by means of semigroup theory and compactness argument,the global existence of the classical solutions with initial data in L1 2.Furthermore,the linear increasing formula of the energy is established.