Global solutions to the Landau-Fermi-Dirac equation
Paulo Sampaio
TL;DR
This paper proves the existence of global weak solutions for the Landau-Fermi-Dirac equation with Coulomb potential by establishing a key compactness result for hypoelliptic equations.
Contribution
It introduces a novel compactness framework that enables the demonstration of global solutions for a complex kinetic equation involving quantum statistics.
Findings
Existence of global weak solutions established.
Compactness result for hypoelliptic equations proved.
Application to Landau-Fermi-Dirac equation with Coulomb potential.
Abstract
We establish a compactness result for solutions of a certain class of hypoelliptic equations. This result allows us to show the existence of global weak solutions to the non-homogeneous Landau-Fermi-Dirac equation with Coulomb potential.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Spectral Theory in Mathematical Physics · Quantum chaos and dynamical systems