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The Landau equation does not blow up

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arxiv 2311.09420 v2 pith:OYGMRSNF submitted 2023-11-15 math.AP

Nestor Guillen , Luis Silvestre This is my paper · ORCID
classification math.AP
keywords equationlandaublowfisherinformationinteractionpotentialssolutions
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We consider solutions to the space-homogeneous Landau equation with a general family of interaction potentials. We prove that their Fisher information is monotone decreasing in time. The class of interaction potentials covered by our result includes the case of the Landau equation with Coulomb interactions. As a consequence of the global boundedness of the Fisher information, we deduce that solutions to the space-homogeneous Landau equation never blow up.

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Cited by 6 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. A structure-preserving local discontinuous Galerkin method for the Fokker-Planck-Landau equation

    math.NA 2025-05 conditional novelty 6.0 of 10

    An upwind LDG scheme for the Fokker-Planck-Landau equation that conserves mass, momentum and a projected energy by building the discrete collision kernel from discrete gradients of the projected energy.

  4. On a fuzzy Landau Equation: Part II. Solvability results

    math.AP 2025-07 conditional novelty 5.0 of 10

    Global existence of entropy-dissipating H-solutions is established for the fuzzy Landau equation with power-law and very-soft kernels, together with a priori propagation estimates for moments and Lp norms.

  5. The Landau equation and Fisher information

    math.AP 2025-07 accept novelty 4.0 of 10

    The Fisher information is non-increasing along solutions of the homogeneous Landau equation with Coulomb potential, ruling out finite-time singularity formation.

  6. Fisher information for solutions of the Boltzmann equation

    math.AP 2025-09 conditional novelty 2.0 of 10

    The Fisher information of the space-homogeneous Boltzmann equation is non-increasing along the flow for all physically relevant kernels, yielding global well-posedness for very soft potentials.

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