Long Time Existence and Asymptotic Behavior of Solutions for the 2D Quasi-geostrophic Equation with Large Dispersive Forcing

Abstract

We consider the initial value problem of the 2D dispersive quasi-geostrophic equation. We prove the long time existence of the solution for given initial data $$\theta _0 \in H^s(\mathbb {R}^2)$$ with $$s>2$$ . Moreover, we show that the solution converges to the corresponding linear dispersive solution $$e^{-AtR_1}\theta _0$$ when the size of dispersion parameter goes to infinity.