Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Institution: Drexel University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7212059835