Frequency Localized Regularity Criteria for the 3D Navier–Stokes Equations

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• 作者：Z. Bradshaw ; Z. Grujić
• 刊名：Archive for Rational Mechanics and Analysis
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：224
• 期：1
• 页码：125-133
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Classical Mechanics; Physics, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Fluid- and Aerodynamics;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-0673
• 卷排序：224

文摘

Two regularity criteria are established to highlight which Littlewood–Paley frequencies play an essential role in possible singularity formation in a Leray–Hopf weak solution to the Navier–Stokes equations in three spatial dimensions. One of these is a frequency localized refinement of known Ladyzhenskaya–Prodi–Serrin-type regularity criteria restricted to a finite window of frequencies, the lower bound of which diverges to \({+\infty}\) as t approaches an initial singular time.