On inhibition of thermal convection instability by a magnetic field under zero resistivity

摘要

We investigate the stability and instability of the magnetic Rayleigh-Benard problem with zero resistivity. A stability criterion is established, under which the magnetic Benard problem is stable. The proof is mainly based on a three-layers energy method and an idea of magnetic inhibition mechanism. The stability result first mathematically verifies Chandrasekhar's physical conjecture in 1955 that the thermal instability can be inhibited by a strong (impressed) magnetic field in magnetohydrodynamic (MHD) fluids with zero resistivity (based on a linearized steady magnetic Benard equations). In addition, we also provide an instability criterion, under which the magnetic Rayleigh-Benard problem is unstable. The instability proof is mainly based on a bootstrap instability method by further developing new techniques. Our instability result shows that the thermal instability still occurs when the (impressed) magnetic field is weak. (C) 2020 Elsevier Masson SAS. All rights reserved.