The Maxwell-Boltzmann approximation for ion kinetic modeling

The aim of this paper is to provide a justification of the Maxwell-Boltzmann approximation of electron density from kinetic models. First, under reasonable regularity assumption, we rigorously derive a reduced kinetic model for the dynamics of ions, while electrons satisfy the Maxwell-Boltzmann relation. Second, we prove that equilibria of the electrons distribution are local Maxwellians, and they can be uniquely determined from conserved mass and energy constants. Finally, we prove that the reduced kinetic model for ions is globally well-posed. The constructed weak solutions conserve energy.