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Theoretical analysis reveals trivial velocity and magnetic field solutions in stationary magnetohydrodynamic systems, indicating expanded uniqueness criteria for mixed local Morrey spaces.
In this paper, we study Liouville theorems for the three-dimensional stationary magnetohydrodynamics (MHD) and Hall magnetohydrodynamics (Hall-MHD) equations in mixed local Morrey spaces. Under some additional hypotheses, we show that the velocity and magnetic field (u,b), belonging to the mixed local Morrey spaces, must be zero. Our theorems extend and improve some recent results.
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