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
Format: Artikel
Sprache:eng
Schlagworte:
incompressible magneto-hydrodynamics (MHD)
Liouville theorem
stream function
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Zusammenfassung: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.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/ac3f8b