  We construct a maximal function associated with a family of skewed cylinders.
These cylinders, which are defined as tubular neighborhoods of trajectories of
a mollified flow, appear in the study of fluid equations such as the
Navier-Stokes equations and the Euler equations. We define a maximal function
subordinate to these cylinders, and show it is of weak type $(1, 1)$ and strong
type $(p, p)$ by a covering lemma. As an application, we give an alternative
proof for the higher derivatives estimate of smooth solutions to the
three-dimensional Navier-Stokes equations.
