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

Diego Chamorro (1) , Oscar Jarrin (1) , Pierre-Gilles Lemarié-Rieusset (1)

1 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry

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 and 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.

Mots clés: Navier–Stokes equations; stationary system; Liouville theorem; Morrey spaces

Domaines: Equations aux dérivées partielles [math.AP]

Diego Chamorro, Oscar Jarrin, Pierre-Gilles Lemarié-Rieusset. Some Liouville theorems for stationary Navier-Stokes equations in Lebesgue and Morrey spaces. 2018. ⟨hal-01802544v1⟩