Calculus of Variations and Geometric Measure Theory

N. De Nitti - F. Hounkpe - S. Schulz

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

created by denitti on 02 Mar 2021
modified on 19 Nov 2022

[BibTeX]

Published Paper

Inserted: 2 mar 2021
Last Updated: 19 nov 2022

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

ArXiv: 2103.00551 PDF

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.