Two improved anisotropic Liouville type theorems for the stationary 3D Navier–Stokes equations

Abstract

In this paper, we establish two new anisotropic Liouville type theorems for the stationary 3D Navier–Stokes equations. Under certain anisotropic integrability conditions on the components of the velocity, we show that the solution is trivial. Our results extend and improve the results of Chae (Appl Math Lett 142:108655, 2023) and Luo and Yin (Arch Ration Mech Anal 224:209–231, 2017).