Behavior of Solutions of 2D Quasi-Geostrophic Equations

Source abstract

We study solutions to the 2D quasi-geostrophic (QGS) equation $$\frac{\partial \theta}{\partial t}+u\cdot\nabla\theta + \kappa (-\Delta)^{\alpha}\theta=f$$ and prove global existence and uniqueness of smooth solutions if $\alpha\in (\frac{1}{2},1]$; weak solutions also exist globally but are proven to be unique only in the class of strong solutions. Detailed aspects of large time approximation by the linear QGS equation are obtained.