Local well-posedness for the incompressible Euler equations in the critical Besov spaces

Zhou, Yong

Local well-posedness for the incompressible Euler equations in the critical Besov spaces
[Bien-posé local pour les équations d'Euler incompressible dans les espaces de Besov critique]

Zhou, Yong

Annales de l'Institut Fourier, Tome 54 (2004), p. 773-786 / Harvested from Numdam

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Abstract

Dans cet article on établit l’existence et l’unicité de la solution locale de l’équation d’Euler incompressible dans $ℝ$ $^{N}$ , $N \geq 3$ , avec des données initiales quelconques appartenant aux espaces de Besov critique $B_{p, 1}^{N / p + 1}$ . De plus, un critère d’explosion est donné en terme du champ de vorticités.

In this paper we establish the existence and uniqueness of the local solutions to the incompressible Euler equations in $ℝ$ $^{N}$ , $N \geq 3$ , with any given initial data belonging to the critical Besov spaces $B_{p, 1}^{N / p + 1}$ . Moreover, a blowup criterion is given in terms of the vorticity field.

Publié le : 2004-01-01

MR 2097422 | Zbl 1097.35118

DOI : https://doi.org/10.5802/aif.2033
Classification: 76D03, 35Q35, 46E35.
Mots clés: bien-posé, equations d'Euler, espaces de Besov

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     author = {Zhou, Yong},
     title = {Local well-posedness for the incompressible Euler equations in the critical Besov spaces},
     journal = {Annales de l'Institut Fourier},
     volume = {54},
     year = {2004},
     pages = {773-786},
     doi = {10.5802/aif.2033},
     mrnumber = {2097422},
     zbl = {1097.35118},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2004__54_3_773_0}
}

Zhou, Yong. Local well-posedness for the incompressible Euler equations in the critical Besov spaces. Annales de l'Institut Fourier, Tome 54 (2004) pp. 773-786. doi : 10.5802/aif.2033. http://gdmltest.u-ga.fr/item/AIF_2004__54_3_773_0/

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