Construction of maximal functions associated with skewed cylinders generated by incompressible flows and applications (Q2693524)

Summary: 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.