Weak-strong uniqueness for the Landau equation by a relative entropy method

Fuente: arXiv
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Autore principale: Tabary, Côme
Natura: Preprint
Pubblicazione: 2025
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author Tabary, Côme
author_facet Tabary, Côme
contents We derive a weak-strong uniqueness and stability principle for the Landau equation in the soft potentials case (including Coulomb interactions). The distance between two solutions is measured by their relative entropy, which to our knowledge was never used before in stability estimates. The logarithm of the strong solution is required to have polynomial growth while the weak solution can be any H-solution with sufficiently many moments at initial time. Since we require a substantial amount of regularity on the strong solution, we also provide an example of sufficient conditions on the initial data that ensure this regularity in the Coulomb (and very soft potentials) case.
format Preprint
id arxiv_https___arxiv_org_abs_2505_21120
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Weak-strong uniqueness for the Landau equation by a relative entropy method
Tabary, Côme
Analysis of PDEs
We derive a weak-strong uniqueness and stability principle for the Landau equation in the soft potentials case (including Coulomb interactions). The distance between two solutions is measured by their relative entropy, which to our knowledge was never used before in stability estimates. The logarithm of the strong solution is required to have polynomial growth while the weak solution can be any H-solution with sufficiently many moments at initial time. Since we require a substantial amount of regularity on the strong solution, we also provide an example of sufficient conditions on the initial data that ensure this regularity in the Coulomb (and very soft potentials) case.
title Weak-strong uniqueness for the Landau equation by a relative entropy method
topic Analysis of PDEs
url https://arxiv.org/abs/2505.21120