Remarks on regularity criteria for the Navier-Stokes equations via one velocity component

Xuanji Jia; Yong Zhou

doi:10.1016/j.nonrwa.2013.08.002

Remarks on regularity criteria for the Navier-Stokes equations via one velocity component

Xuanji Jia, Yong Zhou^*

^*Corresponding author for this work

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

39 Citations (Scopus)

Abstract

Recently, Pokorný and Zhou proved that if ∥u3∥L_∞(0,_T_;L _{(10/3) (R3))}≪ 1 or ∥∇u3∥_L∞(0_,T_;_L _(30/19)_(R3))≪ 1, then the weak solution u of the 3D Navier–Stokes equations is regular on R3 ×(0, T ]. In this paper we remove the smallness assumptions by using a new approach which maybe of independent interest and further application.

Original language	English
Pages (from-to)	239-245
Number of pages	7
Journal	Nonlinear Analysis: Real World Applications
Volume	15
Online published	13 Sept 2013
DOIs	https://doi.org/10.1016/j.nonrwa.2013.08.002
Publication status	Published - Jan 2014

Funding

The authors thank the referee for a careful reading and helpful suggestions. This work is partially supported by Zhejiang Innovation Project (Grant No. T200905), ZJNSF (Grant No. R6090109) and NSFC (Grant No. 10971197).

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WEAK SOLUTIONS

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10.1016/j.nonrwa.2013.08.002

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abstract = "Recently, Pokorn{\'y} and Zhou proved that if ∥u3∥L∞(0,T ;L (10/3) (R3))≪ 1 or ∥∇u3∥L∞(0,T ;L (30/19) (R3))≪ 1, then the weak solution u of the 3D Navier–Stokes equations is regular on R3 ×(0, T ]. In this paper we remove the smallness assumptions by using a new approach which maybe of independent interest and further application.",

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AB - Recently, Pokorný and Zhou proved that if ∥u3∥L∞(0,T ;L (10/3) (R3))≪ 1 or ∥∇u3∥L∞(0,T ;L (30/19) (R3))≪ 1, then the weak solution u of the 3D Navier–Stokes equations is regular on R3 ×(0, T ]. In this paper we remove the smallness assumptions by using a new approach which maybe of independent interest and further application.

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DO - 10.1016/j.nonrwa.2013.08.002

M3 - RGC 21 - Publication in refereed journal

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SP - 239

EP - 245

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

ER -

Remarks on regularity criteria for the Navier-Stokes equations via one velocity component

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