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Peer-reviewedCC BY 4.0SIAM Journal on Mathematical Analysis

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

  • Côme Tabary
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@article{tabary2026weakstrong,
  title = {{Weak-strong uniqueness for the Landau equation by a relative entropy method}},
  author = {Côme Tabary},
  journal = {SIAM Journal on Mathematical Analysis},
  year = {2026},
  month = sep,
  doi = {10.1137/25m178701x},
  eprint = {2505.21120},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05077442v2},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Weak-strong uniqueness for the Landau equation by a relative entropy method
AU  - Côme Tabary
PY  - 2026
DA  - 2026/09/09
JO  - SIAM Journal on Mathematical Analysis
DO  - 10.1137/25m178701x
UR  - https://hal.science/hal-05077442v2
AB  - 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.
SN  - 0036-1410
SN  - 1095-7154
ER  -