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arXiv · 2103.00551

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

Nicola De Nitti·Francis Hounkpe·Simon Schulz
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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.

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Nicola De Nitti, Francis Hounkpe, Simon Schulz. 2021-02-28. On Liouville-type theorems for the 2D stationary MHD equations. https://doi.org/10.1088/1361-6544/ac3f8b

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