an:06605892
Zbl 1344.35080
Hou, Qianqian; Xu, Xiaojing; Ye, Zhuan
Logarithmically improved blow-up criteria for the 3D nonhomogeneous incompressible Navier-Stokes equations with vacuum
EN
Electron. J. Differ. Equ. 2016, Paper No. 192, 12 p. (2016).
00352032
2016
j
35Q30 35B40 76D03 76D05 35B44 35D35
nonhomogeneous Navier-Stokes equations; blow-up criterion; strong solution; vacuum
Summary: 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 \textit{Z. Lei} and \textit{Y. Zhou} [Discrete Contin. Dyn. Syst. 25, No. 2, 575--583 (2009; Zbl 1171.35452)], 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 \(\mathbb R^3\). This results extend recent regularity criterion obtained by \textit{H. Kim} [SIAM J. Math. Anal. 37, No. 5, 1417--1434 (2006; Zbl 1141.35432)].
Zbl 1171.35452; Zbl 1141.35432