有界域中临界 SQG 的全局正则性

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics Pub Date : 2024-07-24 DOI:10.1002/cpa.22221

Peter Constantin, Mihaela Ignatova, Quoc-Hung Nguyen

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引用次数: 0

摘要

我们证明了有界域中临界耗散 SQG 方程全局平稳解的存在性和唯一性。我们引入了一种新方法，将有界域中的单一非局部非线性演化方程转化为整个空间中的扩展非局部非线性演化方程的相互作用系统。然后利用扩展系统中的非局部算子的非线性最大原理方法进行证明。

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Global regularity for critical SQG in bounded domains

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.

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来源期刊

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.