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The Liouville problem for the stationary Navier-Stokes equations on the wholespace is a challenging open problem who has know several recent contributions.We prove here some Liouville type theorems for these equations provided thevelocity field belongs to some Lorentz spaces and then in the more generalsetting of Morrey spaces. Our theorems correspond to a improvement of somerecent result on this problem and contain some well-known results as aparticular case.

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