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Uniqueness of Leray-Hopf weak solutions to the two-dimensional viscous Primitive Equations

  • Jinkai Li
  • Lintao Liu
  • Edriss S. Titi
  • Dong Wang
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Abstract

Global existence of Leray-Hopf (type) weak solutions to the viscous primitive equations in two or three dimensions was established by Lions--Temam--Wang \cite{Lions1,Lions2,Lions3,Lions4} in the 1990s; however, the corresponding uniqueness, no matter in two or three dimensions, has been a long standing open problem since then. In this paper, we solve this open problem in the two-dimensional case. Precisely, we prove the uniqueness of Leray-Hopf weak solutions, with arbitrary L2 initial data, to the viscous primitive equations in a periodic channel, subject to impermeability and stress-free boundary conditions on the solid boundaries.

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Cite

BibTeXRIS
BibTeX
@misc{li2026uniqueness,
  title = {{Uniqueness of Leray-Hopf weak solutions to the two-dimensional viscous Primitive Equations}},
  author = {Jinkai Li and Lintao Liu and Edriss S. Titi and Dong Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11339},
  eprint = {2610.11339},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11339},
}
RIS
TY  - UNPB
TI  - Uniqueness of Leray-Hopf weak solutions to the two-dimensional viscous Primitive Equations
AU  - Jinkai Li
AU  - Lintao Liu
AU  - Edriss S. Titi
AU  - Dong Wang
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.11339
UR  - https://arxiv.org/abs/2610.11339
AB  - Global existence of Leray-Hopf (type) weak solutions to the viscous primitive equations in two or three dimensions was established by Lions--Temam--Wang \cite{Lions1,Lions2,Lions3,Lions4} in the 1990s; however, the corresponding uniqueness, no matter in two or three dimensions, has been a long standing open problem since then. In this paper, we solve this open problem in the two-dimensional case. Precisely, we prove the uniqueness of Leray-Hopf weak solutions, with arbitrary L^2 initial data, to the viscous primitive equations in a periodic channel, subject to impermeability and stress-free boundary conditions on the solid boundaries.
ER  -