Construction of maximal functions associated with skewed cylinders generated by incompressible flows and applications
Jincheng Yang
The University of Texas at Austin, United States of America
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Abstract
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 and strong type 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.
Cite this article
Jincheng Yang, Construction of maximal functions associated with skewed cylinders generated by incompressible flows and applications. Ann. Inst. H. Poincaré Anal. Non Linéaire 39 (2022), no. 4, pp. 793–818
DOI 10.4171/AIHPC/20