On Liouville-type theorems for the 2D stationary MHD equations

Abstract

We establish new Liouville-type theorems for the two-dimensional stationary magneto-hydrodynamic incompressible system assuming that the velocity and magnetic field have bounded Dirichlet integral. The key tool in our proof is observing that the stream function associated to the magnetic field satisfies a simple drift-diffusion equation for which a maximum principle is available.

15 pages

References in corpus (2)

• Liouville type theorems on the steady Navier-Stokes equations in R3
• On Liouville type theorems for the stationary MHD and Hall-MHD systems

Cited by in corpus (1)

• Remarks on Liouville type theorems for the steady MHD and Hall-MHD equations