Qianqian Hou, Xiaojing Xu, Zhuan Ye
Abstract:
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 |
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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 |
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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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