Uniqueness of bounded solutions for the homogeneous Landau equation with a Coulomb potential

Nicolas Fournier

Uniqueness of bounded solutions for the homogeneous Landau equation with a Coulomb potential

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arxiv 0909.0647 v1 pith:VZSL5YOM submitted 2009-09-03 math.AP

Nicolas Fournier This is my paper · ORCID

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keywords solutionsboundedcoulombequationhomogeneouslocalpotentialuniqueness

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We prove the uniqueness of bounded solutions for the spatially homogeneous Fokker-Planck-Landau equation with a Coulomb potential. Since the local (in time) existence of such solutions has been proved by Arsen'ev-Peskov (1977), we deduce a local well-posedness result. The stability with respect to the initial condition is also checked.

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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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