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arXiv · 2610.11339

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 $L^2$ initial data, to the viscous primitive equations in a periodic channel, subject to impermeability and stress-free boundary conditions on the solid boundaries.

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Jinkai Li, Lintao Liu, Edriss S. Titi, Dong Wang. 2026-10-08. Uniqueness of Leray-Hopf weak solutions to the two-dimensional viscous Primitive Equations. https://arxiv.org/abs/2610.11339

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