Some Liouville theorems for stationary Navier-Stokes equations in Lebesgue and Morrey spaces
Diego Chamorro
Laboratoire de Mathématiques et Modélisation d'Evry (LaMME) - UMR 8071, Université d'Evry Val d'Essonne, 23 Boulevard de France, 91037 Evry Cedex, FranceOscar Jarrín
Dirección de investigación y desarrollo (DIDE), Universidad Técnica de Ambato, Avenida de los Chasquis, 180207, Ambato, EcuadorPierre-Gilles Lemarié-Rieusset
Laboratoire de Mathématiques et Modélisation d'Evry (LaMME) - UMR 8071, Université d'Evry Val d'Essonne, 23 Boulevard de France, 91037 Evry Cedex, France
Abstract
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 . Under some additional hypotheses, stated in terms of Lebesgue and Morrey spaces, we will show that the trivial solution is the unique solution. This type of results are known as Liouville theorems.
Cite this article
Diego Chamorro, Oscar Jarrín, Pierre-Gilles Lemarié-Rieusset, Some Liouville theorems for stationary Navier-Stokes equations in Lebesgue and Morrey spaces. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 3, pp. 689–710
DOI 10.1016/J.ANIHPC.2020.08.006