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

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 θ 0 ∈ H s ( R 2 ) with s > 2 . Moreover, we show that the solution converges to the corresponding linear dispersive solution e - A t R 1 θ 0 when the size of dispersion parameter goes to infinity.