Global well-posedness for a slightly supercritical surface quasi-geostrophic equation

Abstract

We use a nonlocal 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 $\theta$ by a Fourier multiplier with symbol $i{k}^{\perp }|k{|}^{-1}m(k|)$, where $m$ is a smooth increasing function that grows slower than $\log \log |k|$ as $|k|\to \infty$.

11 pages, second version with slightly stronger result

References in corpus (2)

• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• Inviscid models generalizing the 2D Euler and the surface quasi-geostrophic equations

Cited by in corpus (7)

• Long time dynamics of forced critical SQG
• On the loss of continuity for super-critical drift-diffusion equations
• Global well-posedness of slightly supercritical active scalar equations
• Absence of anomalous dissipation of energy in forced two dimensional fluid equations
• Stability of Solutions to the Quasi-Geostrophic Equations in ${\mathbb{R}}^2$
• The Optimal Temporal Decay Estimates for the Fractional Power Dissipative Equation in Negative Besov Spaces
• Mild criticality breaking for the Navier-Stokes equations