Regularity criterion for solutions to the three-dimensional Navier Stokes equations in the turbulent channel

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:420

Article

Lin, Hongxia¹  Li, Shan² 

[1] Chengdu Univ Technol, Dept Informat & Comp Sci, Chengdu 610059, Peoples R China

[2] Sichuan Univ, Sch Business, Chengdu 610064, Peoples R China

关键词: Regularity criterion;    Three-dimensional Navier-Stokes equations;    Vertical component of the velocity field;    Strong solution;   

DOI  :  10.1016/j.jmaa.2014.06.026

来源: Elsevier

【 摘 要 】

In this paper, we establish a regularity criterion of solutions to the incompressible Navier Stokes equations in three-dimensional infinite channel in terms of the derivatives of the vertical component of the velocity field. More precisely, we show that the strong solution exists on the time interval [0,T] provided that one of the following conditions holds: partial derivative(u) over bar (3)/partial derivative x(i) is an element of L-q ([0,T]; L-p (Omega)), 1 <= i <= 3 where p > 3, 1 <= q < infinity, 3/p + 2/q <= 1/2 + 3/2p for i = 1,2 and p > 2, 1 <= q < infinity, 3/p + 2/q <= 3/4 + 3/2p for i =3. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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