Liouville theorem of the 3D stationary MHD system: for D-solutions converging to non-zero constant vectors

Abstract

In this paper, we derive the Liouville theorem of D-solutions to the stationary MHD system under the asymptotic assumption: one of the velocity field and the magnetic field approaches zero and the other approaches a non zero constant vector at infinity. Our result extends the corresponding one of D-solutions to the Navier–Stokes equations when the velocity approaches a non zero constant vector at infinity.