An Anisotropic Partial Regularity Criterion for the Navier–Stokes Equations

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• 作者：Igor Kukavica ; Walter Rusin ; Mohammed Ziane
• 刊名：Journal of Mathematical Fluid Mechanics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：19
• 期：1
• 页码：123-133
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Fluid- and Aerodynamics; Mathematical Methods in Physics; Classical and Continuum Physics;
• 出版者：Springer International Publishing
• ISSN：1422-6952
• 卷排序：19

文摘

In this paper, we address the partial regularity of suitable weak solutions of the incompressible Navier–Stokes equations. We prove an interior regularity criterion involving only one component of the velocity. Namely, if (u, p) is a suitable weak solution and a certain scale-invariant quantity involving only u₃ is small on a space-time cylinder \({{Q_{r}^{*}}(x_0,t_0)}\), then u is regular at (x₀, t₀).