Published Paper

Inserted: 2 mar 2021
Last Updated: 19 nov 2022

Journal: Nonlinearity
Year: 2022
Doi: https://doi.org/10.1088/1361-6544/ac3f8b

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.