Some Liouville theorems for stationary Navier-Stokes equations in Lebesgue and Morrey spaces

Chamorro, Diego; Jarrín, Oscar; Lemarié-Rieusset, Pierre-Gilles

doi:10.1016/j.anihpc.2020.08.006

Chamorro, Diego ¹ ; Jarrín, Oscar ² ; Lemarié-Rieusset, Pierre-Gilles ¹

¹ a Laboratoire de Mathématiques et Modélisation d'Evry (LaMME) - UMR 8071, Université d'Evry Val d'Essonne, 23 Boulevard de France, 91037 Evry Cedex, France
² b Dirección de investigación y desarrollo (DIDE), Universidad Técnica de Ambato, Avenida de los Chasquis, 180207, Ambato, Ecuador

Annales de l'I.H.P. Analyse non linéaire, mai – juin 2021, Tome 38 (2021) no. 3, pp. 689-710.

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Résumé

Uniqueness of Leray solutions of the 3D Navier-Stokes equations is a challenging open problem. In this article we will study this problem for the 3D stationary Navier-Stokes equations in the whole space $R^{3}$ . Under some additional hypotheses, stated in terms of Lebesgue and Morrey spaces, we will show that the trivial solution $\vec{U} = 0$ is the unique solution. This type of results are known as Liouville theorems.

MR Zbl

DOI : 10.1016/j.anihpc.2020.08.006

Mots-clés : Navier–Stokes equations, Stationary system, Liouville theorem, Morrey spaces

Affiliations des auteurs :

Chamorro, Diego ¹ ; Jarrín, Oscar ² ; Lemarié-Rieusset, Pierre-Gilles ¹

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     title = {Some {Liouville} theorems for stationary {Navier-Stokes} equations in {Lebesgue} and {Morrey} spaces},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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Chamorro, Diego; Jarrín, Oscar; Lemarié-Rieusset, Pierre-Gilles. Some Liouville theorems for stationary Navier-Stokes equations in Lebesgue and Morrey spaces. Annales de l'I.H.P. Analyse non linéaire, mai – juin 2021, Tome 38 (2021) no. 3, pp. 689-710. doi : 10.1016/j.anihpc.2020.08.006. https://www.numdam.org/articles/10.1016/j.anihpc.2020.08.006/

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