TY - JOUR
T1 - On the nonlinear stability and instability of the boussinesq system for magnetohydrodynamics convection
AU - Bian, Dongfen
N1 - Publisher Copyright:
© 2020 by the authors.
PY - 2020/7/1
Y1 - 2020/7/1
N2 - This paper is concerned with the nonlinear stability and instability of the two-dimensional (2D) Boussinesq-MHD equations around the equilibrium state with the temperature-dependent fluid viscosity, thermal diffusivity and electrical conductivity in a channel. We prove that if small enough constant, and then this equilibrium state is nonlinearly asymptotically stable, and if a+ < a, this equilibrium state is nonlinearly unstable. Here, a+ and a-are the values of the equilibrium temperature θ0(y) on the upper and lower boundary.
AB - This paper is concerned with the nonlinear stability and instability of the two-dimensional (2D) Boussinesq-MHD equations around the equilibrium state with the temperature-dependent fluid viscosity, thermal diffusivity and electrical conductivity in a channel. We prove that if small enough constant, and then this equilibrium state is nonlinearly asymptotically stable, and if a+ < a, this equilibrium state is nonlinearly unstable. Here, a+ and a-are the values of the equilibrium temperature θ0(y) on the upper and lower boundary.
KW - Asymptotic stability
KW - Boussinesq-MHD system
KW - Nonlinear instability
UR - http://www.scopus.com/inward/record.url?scp=85088422749&partnerID=8YFLogxK
U2 - 10.3390/MATH8071049
DO - 10.3390/MATH8071049
M3 - Article
AN - SCOPUS:85088422749
SN - 2227-7390
VL - 8
JO - Mathematics
JF - Mathematics
IS - 7
M1 - 1049
ER -