Preprint
Non-decaying weak solutions to the 2D quasi-geostrophic equations
arXiv (Cornell University)
06 Sep 2026
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 spaceL²_(ul)(ℝ²) . Our methods rely on a spectral Serfati identity, which we use to establish uniformL²_(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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Details
- Title
- Non-decaying weak solutions to the 2D quasi-geostrophic equations
- Creators
- David M Ambrose - Drexel UniversityRyan Aschoff - Google (United States)Elaine Cozzi - Oregon State UniversityJames P Kelliher - University of California, Riverside
- Publication Details
- arXiv (Cornell University)
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991022207141004721