Anisotropic Regularity Conditions for the Suitable Weak Solutions to the 3D Navier–Stokes Equations

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• 作者：Yanqing Wang ; Gang Wu
• 关键词：Navier–Stokes equations ; suitable weak solutions ; regularity
• 刊名：Journal of Mathematical Fluid Mechanics
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：18
• 期：4
• 页码：699-716
• 全文大小：623 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Fluids
  Mathematical Methods in Physics
  Mechanics, Fluids and Thermodynamics
  
• 出版者：Birkh盲user Basel
• ISSN：1422-6952
• 卷排序：18

文摘

We are concerned with the problem, originated from Seregin (159–200, 2007), Seregin (J. Math. Sci. 143: 2961–2968, 2007), Seregin (Russ. Math. Surv. 62:149–168, 2007), what are minimal sufficiently conditions for the regularity of suitable weak solutions to the 3D Navier–Stokes equations. We prove some interior regularity criteria, in terms of either one component of the velocity with sufficiently small local scaled norm and the rest part with bounded local scaled norm, or horizontal part of the vorticity with sufficiently small local scaled norm and the vertical part with bounded local scaled norm. It is also shown that only the smallness on the local scaled L2 norm of horizontal gradient without any other condition on the vertical gradient can still ensure the regularity of suitable weak solutions. All these conclusions improve pervious results on the local scaled norm type regularity conditions.