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

Zhou, Yong

doi:10.5802/aif.2033

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 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)

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

Résumé
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.

MR Zbl

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

Affiliations des auteurs :

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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     title = {Local well-posedness for the incompressible {Euler} equations in the critical {Besov} spaces},
     journal = {Annales de l'Institut Fourier},
     pages = {773--786},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {54},
     number = {3},
     year = {2004},
     doi = {10.5802/aif.2033},
     mrnumber = {2097422},
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     url = {https://www.numdam.org/articles/10.5802/aif.2033/}
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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. https://www.numdam.org/articles/10.5802/aif.2033/

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