GLOBAL WELL-POSEDNESS FOR INHOMOGENEOUS NAVIER-STOKES EQUATIONS WITH LOGARITHMICAL HYPER-DISSIPATION

This paper is devoted to studying the global well-posedness for 3D inhomogeneous logarithmical hyper-dissipative Navier-Stokes equations with dissipative terms D(2)u. Here we consider the supercritical case, namely, the symbol of the Fourier multiplier D takes the form h(xi) = vertical bar xi vertical bar(5/4)/g(xi), where g(xi) = logo (2 + vertical bar xi vertical bar(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) = vertical bar xi vertical bar(5/4).