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

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arxiv 2410.10765 v1 pith:JR53ZC6J submitted 2024-10-14 math.AP math-phmath.MP

Laurent Desvillettes , William Golding , Maria Pia Gualdani , Amelie Loher This is my paper · ORCID
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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].

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Kac's Program for the Landau Equation

    math.AP 2025-06 conditional novelty 8.0 of 10

    The k-particle velocity marginals of Kac's particle system converge to the factorized law of the Landau solution for all power-law potentials, including Coulomb collisions, in weak, Wasserstein, entropic, and strong L...

  2. Weak-strong uniqueness for the Landau equation by a relative entropy method

    math.AP 2025-05 accept novelty 7.0 of 10

    For the Landau equation with soft potentials (including Coulomb), this paper proves that all H-solutions with enough moments coincide with the smooth solution, via a relative entropy estimate.

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

    math.AP 2025-07 conditional novelty 6.0 of 10

    The fuzzy Landau equation has unique global smooth solutions for moderately soft potentials, and its spatial Fisher information decreases monotonically over time.

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