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

Abstract

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 $h(\xi)=|\xi|^{\frac{5}{4}}$.

Locations

• Discrete and Continuous Dynamical Systems - View - PDF