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Existence, uniqueness and smoothing estimates for spatially homogeneous Landau-Coulomb equation in $H^{-\f12}$ space with polynomial tail

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arxiv 2412.07287 v4 pith:WXWSOVRO submitted 2024-12-10 math.AP

Ling-Bing He , Jie Ji , Yue Luo This is my paper · ORCID
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keywords spaceequationestimatesexistencehomogeneouslandau-coulombsmoothingspatially
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abstract

We demonstrate that the spatially homogeneous Landau-Coulomb equation exhibits global existence and uniqueness around the space $H^{-\frac12}_3\cap L^1_{7}\cap L\log L$. Additionally, we furnish several quantitative assessments regarding the smoothing estimates in weighted Sobolev spaces. The new ingredients of the proof lie in the localized techniques in both phase space and frequency space.

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Cited by 4 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. Numerical analysis of the homogeneous Landau equation: approximation, error estimates and simulation

    math.AP 2025-09 conditional novelty 6.0 of 10

    A Fourier spectral scheme for the Landau-Coulomb equation is proven to converge with explicit error bounds: larger truncated domains and more Fourier modes push the error below any prescribed tolerance on any fixed ti...

  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.

  4. The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations

    math.AP 2025-06 reject novelty 6.0 of 10

    For a toy Landau model and a viscous Landau-Coulomb equation, uniqueness of continuous, and conditionally bounded, solutions is proved using a time-averaged negative Sobolev operator.

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