Direction of Vorticity and a Refined Regularity Criterion for the Navier–Stokes Equations with Fractional Laplacian
Tóm tắt
We give a refined regularity criterion for solutions of the three-dimensional Navier–Stokes equations with fractional dissipative term
$$(-\Delta )^{\alpha /2}v$$
. The criterion is composed by the direction field of the vorticity and its magnitude simultaneously. Our result is a generalized of previous results by Beirão da Veiga and Berselli (Differ Integral Equ 15(3):345–356, 2002), and Zhou (ANZIAM J 46(3):309–316, 2005, Monatsh Math 144(3):251–257, 2005). Moreover, our result mentioned about the relation between the solution of the Navier–Stokes equations and the Euler equations.
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