Calculus of Variations and Geometric Measure Theory
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N. De Nitti - F. Hounkpe - S. Schulz

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

created by denitti on 02 Mar 2021


Submitted Paper

Inserted: 2 mar 2021

Year: 2021

ArXiv: 2103.00551 PDF


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.

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