Energy and helicity conservation for the generalized quasi-geostrophic equation

Yanqing Wang, Yulin Ye, Huan Yu

In this paper, we consider the 2-D generalized surface quasi-geostrophic equation with the velocity $v$ determined by $v={\mathcal{R}}^{\perp }{\Lambda }^{\gamma -1}\theta$. It is shown that the $L^p$ ty…