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Entropy dissipation estimates for the Landau equation with Coulomb potentials

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arxiv 2305.09841 v2 pith:7BWCPTA7 submitted 2023-05-16 math.AP

Sehyun Ji This is my paper · ORCID
classification math.AP
keywords coulombdissipationentropyequationlandaulebesguenormpotentials
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abstract

We prove a lower bound for the entropy dissipation of the Landau equation with Coulomb potentials by a weighted Lebesgue norm $L^3_{-5/3}$. In particular, we enhance the weight exponent from $-5$, which was established by Desvillettes, to $-5/3$. Moreover, we prove that the weighted Lebesgue norm $L^3_{-5/3}$ is optimal for both exponents.

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  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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