Global well-posedness for the critical 2D dissipative quasi-geostrophic equation

Abstract

We give an elementary proof of the global well-posedness for the critical 2D dissipative quasi-geostrophic equation. The argument is based on a non-local maximum principle involving appropriate moduli of continuity.

7 pages

References in corpus (1)

• Blow up and regularity for fractal Burgers equation

Cited by in corpus (32)

• Global well-posedness of the critical Burgers equation in critical Besov spaces
• Incompressible Euler Equations: the blow-up problem and related results
• Regularity for a Local-Nonlocal Transmission Problem
• Global wellposedness for the 3D Muskat problem with medium size slope
• Regularity theory for nonlinear integral operators
• On a multi-dimensional transport equation with nonlocal velocity
• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• Hölder continuity of solutions of supercritical dissipative hydrodynamic transport equations
• Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space
• Global well-posedness for the 2 D quasi-geostrophic equation in a critical Besov space
• The vortex patches of Serfati
• Random attractor associated with the quasi-geostrophic equation
• Global regularity for a 1D Euler-alignment system with misalignment
• On a one-dimensional α-patch model with nonlocal drift and fractional dissipation
• Self-similar solutions to the hypoviscous Burgers and SQG equations at criticality
• Global existence for some transport equations with nonlocal velocity
• Fractionally dissipative stochastic quasi-geostrophic type equations on $R^d$
• Eulerian dynamics with a commutator forcing II: flocking
• Suppression of blow up by a logistic source in $2$D Keller-Segel system with fractional dissipation
• Critical SQG in bounded domains
• Global regularity for 1D Eulerian dynamics with singular interaction forces
• The importance of Luis Caffarelli's work in the study of fluids
• On the a priori estimates for the Euler, the Navier-Stokes and the quasi-geostrophic equations
• Remarks on a nonlocal transport
• Remarks on the Global Regularity for the Super-Critical 2D Dissipative Quasi-Geostrophic Equation
• Existence and Uniqueness of Energy Solutions to the Stochastic Diffusive Surface Quasi-Geostrophic Equation with Additive Noise
• A regularity criterion for the dissipative quasi-geostrophic equations
• Estimates of the Green function for the fractional Laplacian perturbed by gradient
• Regularity and blow up for active scalars
• Scaling Limits for Stochastic SQG Equations and 2D Inviscid Critical Boussinesq Equations with Transport Noises
• On a class of forced active scalar equations with small diffusive parameters
• Surface Quasi-Geostrophic Equation driven by Space-Time White Noise