TY - JOUR
T1 - Local-in-time well-posedness for compressible MHD boundary layer
AU - Huang, Yongting
AU - Liu, Cheng-Jie
AU - Yang, Tong
PY - 2019/3/5
Y1 - 2019/3/5
N2 - In this paper, we are concerned with the motion of electrically conducting fluid governed by the two-dimensional non-isentropic viscous compressible MHD system on the half plane with no-slip condition on the velocity field, perfectly conducting wall condition on the magnetic field and Dirichlet boundary condition on the temperature on the boundary. When the viscosity, heat conductivity and magnetic diffusivity coefficients tend to zero in the same rate, there is a boundary layer which is described by a Prandtl-type system. Under the non-degeneracy condition on the tangential magnetic field instead of monotonicity of velocity, by applying a coordinate transformation in terms of the stream function of magnetic field as motivated by the recent work [27], we obtain the local-in-time well-posedness of the boundary layer system in weighted Sobolev spaces.
AB - In this paper, we are concerned with the motion of electrically conducting fluid governed by the two-dimensional non-isentropic viscous compressible MHD system on the half plane with no-slip condition on the velocity field, perfectly conducting wall condition on the magnetic field and Dirichlet boundary condition on the temperature on the boundary. When the viscosity, heat conductivity and magnetic diffusivity coefficients tend to zero in the same rate, there is a boundary layer which is described by a Prandtl-type system. Under the non-degeneracy condition on the tangential magnetic field instead of monotonicity of velocity, by applying a coordinate transformation in terms of the stream function of magnetic field as motivated by the recent work [27], we obtain the local-in-time well-posedness of the boundary layer system in weighted Sobolev spaces.
KW - Boundary layers
KW - Compressible MHD
KW - Local well-posedness
KW - Non-monotonic velocity fields
UR - http://www.scopus.com/inward/record.url?scp=85052950392&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85052950392&origin=recordpage
U2 - 10.1016/j.jde.2018.08.052
DO - 10.1016/j.jde.2018.08.052
M3 - 21_Publication in refereed journal
VL - 266
SP - 2978
EP - 3013
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 6
ER -