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We show that the spatial $L^q$ ($q > 5/3$) norm of the vorticity of anincompressible viscous fluid in $\mathbb{R}^3$ or $\mathbb{T}^3$ remainsbounded uniformly in time, provided that the direction of vorticity is H\"oldercontinuous in the space variable, and that the space--time $L^q$ norm of thevorticity is finite. The H\"older index depends only on $q$. This serves as avariant of the classical result by P. Constantin and Ch. Fefferman (Directionof vorticity and the problem of global regularity for the Navier--Stokesequations, Indiana Univ. J. Math., 42 (1993), 775--789).

On Vortex Alignment and Boundedness of $L^q$ Norm of Vorticity