Abstract
In \cite{YZ}, the author proved the global existence of the two-dimensional anisotropic quasi-geostrophic equations with condition on the parameters \(\alpha,\) \(\beta\) in the Sobolev spaces \(H^s( \R^2)\); \(s\geq 2\). In this paper, we show that this equations has a global solution in the spaces \(H^s(\R^2)\), where \(\max\{2-2\alpha,2-2\beta\}< s<2\), with additional condition over \(\alpha\) and \(\beta\). The proof is based on the Gevrey-class regularity of the solution in neighborhood of zero.