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Global solutions to the Landau-Fermi-Dirac equation

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arxiv 2410.12681 v1 pith:WLLZJM7A submitted 2024-10-16 math.AP

Paulo Sampaio This is my paper · ORCID
classification math.AP
keywords solutionsequationgloballandau-fermi-diracresultallowscertainclass
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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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Cited by 2 Pith papers

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  1. Nonlinear quantum Fokker-Planck equation near equilibrium

    math.AP 2026-07 accept novelty 7.0 of 10

    For small smooth perturbations of the global quantum equilibrium, the self-consistent nonlinear quantum Fokker–Planck equation has a unique global strong solution with algebraic decay to equilibrium.

  2. On the semi-classical limit for the Landau-Fermi-Dirac equation

    math.AP 2025-01 conditional novelty 7.0 of 10

    Sequences of suitable weak solutions of the Landau-Fermi-Dirac equation converge, up to subsequence, to Villani renormalized solutions of the classical Landau equation in the vanishing quantum parameter limit.

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