Liouville Theorems for the Stationary Fractional Hall-Magnetohydrodynamic Equations

In this paper we prove Liouville-type theorems for the stationary fractional Hall-magnetohydrodynamic equations in R³. Smooth solutions vanishing at infinity, with u∈ Hα/2 and b∈ Hβ/2, are trivial for 1≤α≤53, 1≤β<2 and α+2β≤5, with no additional integrability assumption. The key step is to estimate the Hall boundary term through the Caffarelli--Silvestre extension of b.