Large-Time Behaviour of Solutions to the Surface Quasi-Geostrophic Equations

Abstract

We construct a linear approximation of the solution to the Surface Quasi-Geostrophic Equation in ${\mathbb{R}}^2$, and obtain a convergence rate in $L^p$ between the solution and this approximation with respect to time. We also demonstrate that the nonlinear term of the solution is bounded sharply in $L^p$ by the same function of time.

References in corpus (2)

• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• Energy Spectrum of Quasi-Geostrophic Turbulence