Geodesic
Some Liouville theorems for stationary Navier-Stokes equations in Lebesgue and Morrey spaces
Chamorro, Diego1 ; Jarrín, Oscar2 ; Lemarié-Rieusset, Pierre-Gilles1 idref
1a Laboratoire de Mathématiques et Modélisation d'Evry (LaMME) - UMR 8071, Université d'Evry Val d'Essonne, 23 Boulevard de France, 91037 Evry Cedex, France
2b 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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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 R3. Under some additional hypotheses, stated in terms of Lebesgue and Morrey spaces, we will show that the trivial solution U→=0 is the unique solution. This type of results are known as Liouville theorems.

DOI : 10.1016/j.anihpc.2020.08.006
Keywords: Navier–Stokes equations, Stationary system, Liouville theorem, Morrey spaces

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 
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     author = {Chamorro, Diego and Jarr{\'\i}n, Oscar and Lemari\'e-Rieusset, Pierre-Gilles},
     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},
     pages = {689--710},
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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

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