Regresar

A remark on the Liouville problem for stationary Navier-Stokes equations in Lorentz and Morrey spaces

Abstract:

The Liouville problem for the stationary Navier-Stokes equations on the whole space is a challenging open problem who has known several recent contributions. We prove here some Liouville type theorems for these equations provided the velocity field belongs to some Lorentz spaces and then in the more general setting of Morrey spaces. Our theorems correspond to an improvement of some recent results on this problem and contain some well-known results as a particular case.