no. 4
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 
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     author = {Yang, Jincheng},
     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},
     url = {https://www.numdam.org/articles/10.4171/aihpc/20/}
}
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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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