Liouville‐type theorem for the steady compressible Hall‐MHD system

Abstract

In this paper, we prove a Liouville-type theorem for the steady compressible Hall-magnetohydrodynamics system in Π, where Π is whole space R 3 or half space R 3 + . We show that a smooth solution ( , u, B, P), and B ∈ L 9/2 (Π) for some constant C 0 > 0 is indeed trivial. This generalizes and improves 2 results of Chae.

Liouville type Theorems for the stationary compressible 3D MHD equations

“…We think it is secondary to consider the Hall term in the system (1.1). Considering the Hall term, curl × (curlb × b) in (1.1), namely, (compressible) Hall-MHD equations, we can see that additional conditions are required for the magnetic filed b in light of the references [33], [30] and [18]. Proofs of this part is not difficult, and thus leave it to the readers.…”