SQG流的规律性、唯一性及小尺度和大尺度的相对大小

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics Pub Date : 2025-06-30 DOI:10.1007/s00021-025-00947-x

Z. Akridge, Z. Bradshaw

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引用次数: 0

摘要

研究了一类超临界耗散曲面拟地转方程的正则性和唯一性问题。在这篇笔记中，我们研究了小尺度或大尺度在假设的爆炸场景中的温度和假设的非唯一性场景中的误差中必须活跃的程度，后者在马尔尚解的类别中被理解。这扩展了先前对三维Navier-Stokes方程的研究。对于超临界SQG，温和溶液技术是不可用的，这使得扩展变得复杂。这迫使我们利用能量方法和Littlewood-Paley理论开发一种新的方法。

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Regularity, Uniqueness and the Relative Size of Small and Large Scales in SQG Flows

The problems of regularity and uniqueness are open for the supercritically dissipative surface quasi-geostrophic equations in certain classes. In this note we examine the extent to which small or large scales are necessarily active both for the temperature in a hypothetical blow-up scenario and for the error in hypothetical non-uniqueness scenarios, the latter understood within the class of Marchand’s solutions. This extends prior work for the 3D Navier-Stokes equations. The extension is complicated by the fact that mild solution techniques are unavailable for supercritical SQG. This forces us to develop a new approach using energy methods and Littlewood-Paley theory.

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来源期刊

Journal of Mathematical Fluid Mechanics 物理-力学

CiteScore

2.00

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.