We prove the existence and uniqueness of global smooth solutions of the critical dissipative SQG equation in bounded domains in . We introduce a new methodology of transforming the single nonlocal nonlinear evolution equation in a bounded domain into an interacting system of extended nonlocal nonlinear evolution equations in the whole space. The proof then uses the method of the nonlinear maximum principle for nonlocal operators in the extended system.

中文翻译：

---

有界域中关键 SQG 的全局正则性


我们证明了有界域中临界耗散 SQG 方程的全局光滑解的存在性和唯一性。我们引入了一种新的方法，将有界域中的单个非局部非线性演化方程转换为整个空间中扩展非局部非线性演化方程的相互作用系统。然后使用非线性极大值原理的方法来证明扩展系统中的非局部算子。