Electron. J. Diff. Equ., Vol. 2016 (2016), No. 192, pp. 1-12.

Logarithmically improved blow-up criteria for the 3D nonhomogeneous incompressible Navier-Stokes equations with vacuum

Qianqian Hou, Xiaojing Xu, Zhuan Ye

This article is devoted to the study of the nonhomogeneous incompressible Navier-Stokes equations in space dimension three. By making use of the "weakly nonlinear" energy estimate approach introduced by Lei and Zhou in [16], we establish two logarithmically improved blow-up criteria of the strong or smooth solutions subject to vacuum for the 3D nonhomogeneous incompressible Navier-Stokes equations in the whole space R^3. This results extend recent regularity criterion obtained by Kim (2006) [13].

Submitted April 29, 2015. Published July 14, 2016.
Math Subject Classifications: 35Q30, 35B40, 76D03, 76D05.
Key Words: Nonhomogeneous Navier-Stokes equations; blow-up criterion; strong solution; vacuum.

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Qianqian Hou
Department of Applied Mathematics
Hong Kong Polytechnic University
Hung Hom, Kowloon, Hong Kong
email: qianqian.hou@connect.polyu.hk
Xiaojing Xu
School of Mathematical Sciences
Beijing Normal University
Laboratory of Mathematics and Complex Systems
Ministry of Education
Beijing 100875, China
email: xjxu@bnu.edu.cn
Zhuan Ye
Department of Mathematics and Statistics
Jiangsu Normal University
101 Shanghai Road
Xuzhou 221116, Jiangsu, China
email: yezhuan815@126.com

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