PreprintCC BY 4.0arXiv
Non-decaying weak solutions to the 2D quasi-geostrophic equations
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 L2ul(ℝ2). Our methods rely on a spectral Serfati identity, which we use to establish uniform L2ul 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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BibTeX
@misc{ambrose2026nondecaying,
title = {{Non-decaying weak solutions to the 2D quasi-geostrophic equations}},
author = {David M. Ambrose and Ryan Aschoff and Elaine Cozzi and James P. Kelliher},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06836},
eprint = {2609.06836},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06836},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-decaying weak solutions to the 2D quasi-geostrophic equations
AU - David M. Ambrose
AU - Ryan Aschoff
AU - Elaine Cozzi
AU - James P. Kelliher
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06836
UR - https://arxiv.org/abs/2609.06836
AB - 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(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.
ER -