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December  2016, 36(12): 6921-6941. doi: 10.3934/dcds.2016101

## Global well-posedness for inhomogeneous Navier-Stokes equations with logarithmical hyper-dissipation

 1 Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China 2 Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, China

Received  October 2015 Revised  August 2016 Published  October 2016

This paper is devoted to studying the global well-posedness for 3D inhomogeneous logarithmical hyper-dissipative Navier-Stokes equations with dissipative terms $D^2u$. Here we consider the supercritical case, namely, the symbol of the Fourier multiplier $D$ takes the form $h(\xi)=|\xi|^{\frac{5}{4}}/g(\xi)$, where $g(\xi)=\log^{\frac{1}{4}}(2+|\xi|^2)$. This generalizes the work of Tao [17] to the inhomogeneous system, and can also be viewed as a generalization of Fang and Zi [12], in which they considered the critical case $h(\xi)=|\xi|^{\frac{5}{4}}$.
Citation: Bin Han, Changhua Wei. Global well-posedness for inhomogeneous Navier-Stokes equations with logarithmical hyper-dissipation. Discrete & Continuous Dynamical Systems - A, 2016, 36 (12) : 6921-6941. doi: 10.3934/dcds.2016101
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