[Existence de solutions fortes globales pour le système de Navier–Stokes compressible avec des données initiales grandes sur la partie rotationnelle de la vitesse]
Nous montrons lʼexistence de solutions fortes globales pour le système de Navier–Stokes compressible en dimension avec des données initiales grandes sur la partie rotationnelle de la vitesse. Suivant Chemin et Gallagher (2009, 2011) [3,4], nous cherchons a exhiber des données initiales telles que la projection sur les champs de vecteurs à divergence nulle soient grandes dans (qui est le plus large espace invariant par le scaling des équations) et telle que ces données initiales génèrent des solutions fortes globales. Le fait que lʼhypothèse de petitesse dans Chemin et Gallagher (2009) [3] a lieu sur le terme non linéaire de convection nous permet de décomposer la solution des équations de Navier–Stokes compressible comme la somme dʼune vitesse incompressible et dʼune vitesse purement compressible. Combinant la notion de quasi-solution introduite dans Haspot [8,9,7], nous obtenons lʼexistence de solutions fortes globales avec des données initiales à la fois grande pour la partie irrationnelle et la partie rotationnelle.
We show the existence of global strong solutions for the compressible Navier–Stokes system in dimension with large initial data on the rotational part of the velocity. By following Chemin and Gallagher (2009, 2011) [3,4], we aim at exhibiting large initial data such that the projection on the divergence field is large in (which is the largest space invariant by the scaling of the equations) and such that these initial data generate global strong solution. The fact that the smallness hypothesis in Chemin and Gallagher (2009) [3] holds on the nonlinear term of convection enables us to split the solution of the compressible Navier–Stokes equations in the sum of an incompressible solution and of a purely compressible solution. Combining the notion of quasi-solution introduced in Haspot [8,9,7], we obtain the existence of global strong solution for the shallow water system for large initial velocity both on the irrotational and rotational part.
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@article{CRMATH_2012__350_9-10_487_0,
author = {Boris Haspot},
title = {Existence of global strong solutions for the barotropic {Navier{\textendash}Stokes} system with large initial data on the rotational part of the velocity},
journal = {Comptes Rendus. Math\'ematique},
pages = {487--492},
publisher = {Elsevier},
volume = {350},
number = {9-10},
year = {2012},
doi = {10.1016/j.crma.2012.04.017},
language = {en},
}
TY - JOUR AU - Boris Haspot TI - Existence of global strong solutions for the barotropic Navier–Stokes system with large initial data on the rotational part of the velocity JO - Comptes Rendus. Mathématique PY - 2012 SP - 487 EP - 492 VL - 350 IS - 9-10 PB - Elsevier DO - 10.1016/j.crma.2012.04.017 LA - en ID - CRMATH_2012__350_9-10_487_0 ER -
%0 Journal Article %A Boris Haspot %T Existence of global strong solutions for the barotropic Navier–Stokes system with large initial data on the rotational part of the velocity %J Comptes Rendus. Mathématique %D 2012 %P 487-492 %V 350 %N 9-10 %I Elsevier %R 10.1016/j.crma.2012.04.017 %G en %F CRMATH_2012__350_9-10_487_0
Boris Haspot. Existence of global strong solutions for the barotropic Navier–Stokes system with large initial data on the rotational part of the velocity. Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, pp. 487-492. doi : 10.1016/j.crma.2012.04.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.04.017/
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