The Role of the Dimension in Uniqueness Results for the Fractional Stationary Quasi-Geostrophic System

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-06-25 DOI:10.1002/mma.11170

Diego Chamorro, Manuel Fernando Cortez

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引用次数: 0

Abstract

In this paper, we study a Liouville-type theorem for the stationary fractional quasi-geostrophic equation in various dimensions. Indeed, our analysis focuses essentially on dimensions $n = 2, 3, 4$ , and we explore the uniqueness of weak solutions for this fractional system. We demonstrate here that, under some specific Lebesgue integrability information, the only admissible solution to the stationary fractional quasi-geostrophic system is the trivial one, and this result provides a comprehensive understanding of how the dimension, in connection to the fractional power of the Laplacian, influences the uniqueness properties of weak solutions.

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分数阶平稳准地转系统维数在唯一性结果中的作用

本文研究了多维平稳分数阶拟地转方程的一个liouville型定理。事实上，我们的分析主要集中在维度n = 2,3,4上。2,3,4 $$，我们探讨了这个分数阶系统弱解的唯一性。在某些特定的Lebesgue可积性信息下，我们证明了平稳分数阶拟地转系统的唯一可容许解是平凡解，这一结果提供了一个关于拉普拉斯函数分数阶幂的维数如何影响弱解的唯一性的全面理解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.