各向异性Sobolev空间中分数阶拟地转方程的稳定性
Stability Results of Fractional Surface Quasi-Geostrophic Equation in Anisotropic Sobolev Space

本文针对二维分数阶表面准地转SQG方程的存在全局解，在初始数据${\theta }_0$ 属于非齐次各向异性Sobolev空间$H^{0,\alpha }\left(\frac{1}{2}<\alpha <1\right)$ 条件下，利用Bony分解理论和Littlewood-Paley分解技术，证明了该方程解的稳定性。
We prove the stability of a global solution for the fractional SQG equation under the conditions that the initial data ${\theta }_0$ belongs to the nonhomogeneous anisotropic Sobolev space $H^{0,\alpha }$ with $\frac{1}{2}<\alpha <1$ . The main tools employed in our analysis are the Bony decomposition theory and Littlewood-Paley decomposition technique.