The fuzzy Landau equation: global well-posedness and Fisher information

TL;DR

This paper introduces a fuzzy version of the inhomogeneous Landau equation, proving global existence and uniqueness of smooth solutions, and analyzing Fisher information decay to understand the model's structural properties.

Contribution

It presents a novel fuzzy Landau equation model with proven global well-posedness and insights into Fisher information behavior, highlighting the effects of spatial delocalization.

Findings

Global existence and uniqueness of smooth solutions

Monotonic decay or boundedness of Fisher information

Enhanced regularity due to spatial delocalization

Abstract

We study a fuzzy variant of the inhomogeneous Landau equation and establish global-in-time existence and uniqueness of smooth solutions for moderately soft potentials. The spatial delocalization introduced in the collision operator not only enhances regularity and prevents singularity formation, but also reveals additional structural properties of the model. In particular, we show that several forms of the Fisher information decay monotonically or remain uniformly bounded in time.