Journal
BANACH JOURNAL OF MATHEMATICAL ANALYSIS
Volume 17, Issue 1, Pages -Publisher
SPRINGER BASEL AG
DOI: 10.1007/s43037-022-00236-z
Keywords
Liouville-type theorems; Hall-MHD equations; MHD equations
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The paper studies the Liouville-type problem for three-dimensional stationary incompressible inhomogeneous MHD and Hall-MHD equations without any integrability condition for (del u, del B). Specifically, it demonstrates that the velocity field u and the magnetic field B, which satisfy suitable growth conditions for the mean oscillations of potential functions at infinity, are zero when the density rho is essentially bounded.
The present paper is devoted to the Liouville-type problem for the three-dimensional stationary incompressible inhomogeneous MHD and Hall-MHD equations without any integrability condition for (del u,del B). More precisely, we show that the velocity fieldu and the magnetic field B, satisfying some suitable growth conditions at infin-ity for the mean oscillations of the potential functions, are identically equal to zero provided that the density rho is essentially bounded.
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