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]
Annales de l'Institut Fourier, Tome 54 (2004) no. 3, pp. 773-786.

Dans cet article on établit l’existence et l’unicité de la solution locale de l’équation d’Euler incompressible dans N , N3, 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 N , N3, 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.

DOI : 10.5802/aif.2033
Classification : 76D03, 35Q35, 46E35.
Keywords: well-posedness, Euler equations, Besov spaces
Mot clés : bien-posé, equations d'Euler, espaces de Besov
Zhou, Yong 1

1 Chinese University of Hong Kong, Institute of Mathematical Sciences and Department of Mathematics, Shatin, N.T. (Hong Kong), Xiamen University, Xiamen, Fujian (Chine)
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Zhou, Yong. Local well-posedness for the incompressible Euler equations in the critical Besov spaces. Annales de l'Institut Fourier, Tome 54 (2004) no. 3, pp. 773-786. doi : 10.5802/aif.2033. http://www.numdam.org/articles/10.5802/aif.2033/

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