Global existence of classical solutions to the Fokker-Planck-BGK equation

作者：Zhang Xianwen^*

来源：Journal of Statistical Physics, 2008, 132(3): 535-550.

DOI：10.1007/s10955-008-9546-7

• Fokker-Planck-BGK equation
• initial value problem
• classical solution
• local Maxwellian

A kinetic model of the Fokker-Planck-Boltzmann equation is introduced by replacing the original Boltzmann collision operator with the Bhatnagar-Gross-Krook collision model (BGK collision model). This model equation, which we call the Fokker-Planck-BGK equation, has many physical features that the Fokker-Planck-Boltzmann equation possesses. We first establish an L(infinity) existence result for this equation, by which we construct the approximate solutions. Then, by means of the regularizing effects of the linear Fokker-Planck operator and L(p) estimates of local Maxwellians, we obtain some uniform estimates of the approximate solutions. Finally, combining those estimates and regularizing effects, we prove by a compactness argument that the equation has a global classical solution under rather general initial conditions.

• 出版日期2008-8
• 单位华中科技大学