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arXiv · 2609.06836

Non-decaying weak solutions to the 2D quasi-geostrophic equations

David M. Ambrose·Ryan Aschoff·Elaine Cozzi·James P. Kelliher
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Abstract

We investigate weak solutions to the two-dimensional quasi-geostrophic equations without dissipation. We establish global existence of weak solutions for temperature bounded and lacking spatial decay and velocity in the space $L^2_{ul}(\mathbb{R}^2)$. Our methods rely on a spectral Serfati identity, which we use to establish uniform $L^2_{ul}$ bounds on a sequence of velocities satisfying the dissipative equations. These bounds, combined with a maximum principle on the scalar temperature, allow us to pass to the zero-dissipation limit, giving global-in-time weak solutions.

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David M. Ambrose, Ryan Aschoff, Elaine Cozzi, James P. Kelliher. 2026-09-06. Non-decaying weak solutions to the 2D quasi-geostrophic equations. https://arxiv.org/abs/2609.06836

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