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Entropy dissipation estimates for the Landau equation in the Coulomb case and applications

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arxiv 1408.6025 v2 pith:ZHR6LCTX submitted 2014-08-26 math.AP

Laurent Desvillettes This is my paper · ORCID
classification math.AP
keywords equationlandaucoulombestimatedissipationentropyinteractionweighted
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We present in this paper an estimate which bounds from below the entropy dissipation D(f) of the Landau operator with Coulomb interaction by a weighted H^1 norm of the square root of f. As a consequence, we get a weighted L^1_t(L^3_v) estimate for the solutions of the spatially homogeneous Landau equation with Coulomb interaction, and the propagation of L^1 moments of any order for this equation. We also present an application of our estimate to the Landau equation with (moderately) soft potentials, providing thus a new proof of some recent results of Kung-Chien Wu

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 82 citations worldwide. Full citation record

  1. 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.

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