The Liouville theorems for 3D stationary inhomogeneous incompressible MHD equations

We consider the Liouville theorems for the 3D stationary inhomogeneous incompressible MHD equations. Specifically, we prove that if $(\rho ,u,b)$ satisfies some integrable conditions in the Lebesgue, Lorentz and local Morrey spaces, then the solution is trivial. Our results generalize and improve the corresponding results of P. Liu [J. Math. Anal. Appl. 521 (2023), art. 126945].