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

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

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 satis...

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Veröffentlicht in:Nonlinearity 2022-02, Vol.35 (2), p.870-888
Hauptverfasser: De Nitti, Nicola, Hounkpe, Francis, Schulz, Simon
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incompressible magneto-hydrodynamics (MHD)
Liouville theorem
stream function
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Hounkpe, Francis
Schulz, Simon
description 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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subjects incompressible magneto-hydrodynamics (MHD)
Liouville theorem
stream function
title On Liouville-type theorems for the 2D stationary MHD equations
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