Production of the Fisher information for the Landau-Coulomb equation with L1 initial data

TL;DR

This paper proves the existence of global solutions with bounded Fisher information for the Landau-Coulomb equation starting from L1 initial data, advancing understanding of solution regularity over time.

Contribution

It introduces an alternative method to establish the emergence of Fisher information in solutions to the Landau-Coulomb equation, building on existing estimates.

Findings

Existence of global weak solutions with bounded Fisher information

Solutions become strong solutions away from initial time

Provides a new approach to study Fisher information appearance

Abstract

We consider the Landau-Coulomb equation for initial data with bounded mass, finite numbers of moments, and entropy. We show the existence of a global weak solution that has bounded Fisher information for positive times. This solution is therefore a global strong solution away from the initial time. We propose an alternative approach, based on already existing estimates, to the study of the appearance of Fisher information recently performed by Ji in [12].