Liouville-type theorems for the stationary incompressible inhomogeneous Hall-MHD and MHD equations

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.

Automated summary

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.