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

TL;DR

This paper investigates the transition from non-cutoff fuzzy Boltzmann equations to fuzzy Landau equations in the grazing collision limit, using variational formulations linked to GENERIC structures.

Contribution

It demonstrates the convergence of variational formulations from fuzzy Boltzmann to fuzzy Landau equations, highlighting the change from non-quadratic to quadratic dissipation pairs.

Findings

Grazing limit from fuzzy Boltzmann to fuzzy Landau equations established.

Variational formulations converge under the grazing collision limit.

Transition from non-quadratic to quadratic dissipation pairs shown.

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.