We use a non-local maximum principle to prove the global existence of smooth solutions for a slightly supercritical surface quasi-geostrophic equation. By this we mean that the velocity field u is obtained from the active scalar by a Fourier multiplier with symbol iζ ⊥|ζ| -1m(|ζ|), where m is a smooth increasing function that grows slower than log log|ζ| as |ζ| → ∞.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics