Regularity criterion to the axially symmetric Navier-Stokes equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:435

Article

Wei, Dongyi^1,2 

[1] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

[2] Peking Univ, BICMR, Beijing 100871, Peoples R China

关键词: Axially symmetric;    Navier-Stokes equations;    Regularity criterion;   

DOI  :  10.1016/j.jmaa.2015.09.088

来源: Elsevier

【 摘 要 】

Smooth solutions to the axially symmetric Navier-Stokes equations obey the following maximum principle: parallel to ru(theta) (r, z, t)parallel to(L infinity) <= parallel to ru(theta) (r, z, 0)parallel to(L infinity). We first prove the global regularity of solutions if parallel to ru(theta) (r, z, 0)parallel to(L infinity) or parallel to ru(theta) (r, z, t)parallel to(L infinity(r <= r0)) is small compared with certain dimensionless quantity of the initial data. This result improves the one in Zhen Lei and Qi S. Zhang [10]. As a corollary, we also prove the global regularity under the assumption that} vertical bar ru(theta)(r,z,t)vertical bar <= vertical bar ln r vertical bar(-3/2), for all 0 < r <= delta(0) is an element of (0,1/2). (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free