On a fuzzy Landau Equation: Part I. A variational approach

This article is the first in a series of works on the fuzzy Landau equation, where particles interact through delocalised Coulomb collisions. Here, we establish a variational characterisation that recasts the fuzzy Landau equation within the framework of GENERIC systems (General Equations for Non-Equilibrium Reversible-Irreversible Coupling).

💡 Research Summary

This paper introduces and studies a “fuzzy” version of the Landau kinetic equation, in which particle collisions are allowed to occur at different spatial locations, weighted by a spatial kernel κ. The authors consider the inhomogeneous kinetic equation

∂ₜf + v·∇ₓf = Q_fuz(f,f) , f(0)=f₀,

with the collision operator

Q_fuz(f,f)(x,v) = ∇v·∫{Ω×ℝ^d} κ(x−x*) a(v−v*)