Geodesic
Construction of maximal functions associated with skewed cylinders generated by incompressible flows and applications
Annales de l'I.H.P. Analyse non linéaire, Tome 39 (2022) no. 4, pp. 793-818

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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.

Accepté le :
Publié le :
DOI : 10.4171/aihpc/20
Classification : 42B25, 76D05, 35Q30
Keywords: maximal function, covering lemma, Incompressible flows, Lagrangian/Eulerian representation, Partial regularity 
Yang, Jincheng. Construction of maximal functions associated with skewed cylinders generated by incompressible flows and applications. Annales de l'I.H.P. Analyse non linéaire, Tome 39 (2022) no. 4, pp. 793-818. doi: 10.4171/aihpc/20
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     title = {Construction of maximal functions associated with skewed cylinders generated by incompressible flows and applications},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {793--818},
     year = {2022},
     volume = {39},
     number = {4},
     doi = {10.4171/aihpc/20},
     language = {en},
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