We prove the existence and uniqueness of global smooth solutions of the critical dissipative SQG equation in bounded domains in R^2. 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.

Publication:

Communications on Pure and Applied Mathematics 17 June 2024

https://doi.org/10.1002/cpa.22221

Author:

Peter Constantin

Department of Mathematics, Princeton University, Princeton, New Jersey, USA

Email: const@math.princeton.edu

Mihaela Ignatova

Department of Mathematics, Temple University, Philadelphia, Pennsylvania, USA

Quoc-Hung Nguyen

Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China