Dans cette Note, nous donnons des conditions suffisantes de régularité des solutions des équations de Navier–Stokes. Nous montrons que si une solution de Leray–Hopf vérifie l'une des trois conditions (i) où et , (ii) où et , ou (iii) où et , alors elle est régulière. Ces conditions améliorent les résultats existants sur la régularité conditionnelle des équations de Navier–Stokes.
In this Note, we give sufficient conditions for the regularity of Leray–Hopf weak solutions to the Navier–Stokes equation. We prove that, if one of three conditions (i) where and , (ii) where and , or (iii) where and , is satisfied, then the solution is regular. These conditions improve earlier results on the conditional regularity of the Navier–Stokes equations.
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@article{CRMATH_2006__343_1_31_0,
author = {Igor Kukavica and Mohammed Ziane},
title = {R\'egularit\'e conditionnelle des \'equations de {Navier{\textendash}Stokes}},
journal = {Comptes Rendus. Math\'ematique},
pages = {31--36},
publisher = {Elsevier},
volume = {343},
number = {1},
year = {2006},
doi = {10.1016/j.crma.2006.04.024},
language = {fr},
}
Igor Kukavica; Mohammed Ziane. Régularité conditionnelle des équations de Navier–Stokes. Comptes Rendus. Mathématique, Volume 343 (2006) no. 1, pp. 31-36. doi : 10.1016/j.crma.2006.04.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.04.024/
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