We consider classical solutions of the inviscid Surface Quasi-geostrophic equation that are a small perturbation ϵ from a radial stationary solution $\theta =|x|$. We use a modified energy method to prove the existence time of classical solutions from $\frac{1}{ϵ}$ to a time scale of $\frac{1}{{ϵ}^4}$. Moreover, by perturbing in a suitable direction we construct global smooth solutions, via bifurcation, that rotate uniformly in time and space.

中文翻译：

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无粘表面准地转方程经典解的寿命

我们考虑无粘性表面准地转方程的经典解，它是来自径向平稳解的小扰动ϵ$\theta =|X|$. 我们使用修正能量法来证明经典解的存在时间$\frac{1}{\epsilon }$ 到一个时间尺度 $\frac{1}{{\epsilon }^4}$. 此外，通过在合适的方向上扰动，我们通过分叉构建了在时间和空间上均匀旋转的全局平滑解。