On a fuzzy Landau Equation: Part III. The grazing collision limit

Abstract

In this paper, we study the grazing limit from the non-cutoff fuzzy Boltzmann equations to the fuzzy Landau equation, where particles interact through delocalised collisions. We show the grazing limit through variational formulations that correspond to the GENERIC (General Equations for Non-Equilibrium Reversible-Irreversible Coupling) structure of the respective equations. We show that the variational formulation associated with a non-quadratic dual dissipation pair for the fuzzy Boltzmann equations converges to a variational formulation of the fuzzy Landau equation corresponding to a quadratic dissipation pair.