TY - JOUR
T1 - UNIFORM REGULARITY AND VANISHING VISCOSITY LIMIT FOR THE INCOMPRESSIBLE NON-RESISTIVE MHD SYSTEM WITH TRANSVERSE MAGNETIC FIELD
AU - LIU, Cheng-Jie
AU - XIE, Feng
AU - YANG, Tong
PY - 2021/7
Y1 - 2021/7
N2 - This paper is concerned with the vanishing viscosity limit for the incompressible MHD system without magnetic diffusion effect in the half space under the influence of a transverse magnetic field on the boundary. We prove that the solution to the incompressible MHD system is uniformly bounded in both conormal Sobolev norm and L∞ norm in a fixed time interval independent of the viscosity coefficient. As a direct consequence, the inviscid limit from the viscous MHD system to the ideal MHD system is established in L∞-norm. In addition, the analysis shows that the boundary layer effect is weak because of the transverse magnetic field.
AB - This paper is concerned with the vanishing viscosity limit for the incompressible MHD system without magnetic diffusion effect in the half space under the influence of a transverse magnetic field on the boundary. We prove that the solution to the incompressible MHD system is uniformly bounded in both conormal Sobolev norm and L∞ norm in a fixed time interval independent of the viscosity coefficient. As a direct consequence, the inviscid limit from the viscous MHD system to the ideal MHD system is established in L∞-norm. In addition, the analysis shows that the boundary layer effect is weak because of the transverse magnetic field.
KW - Incompressible non-resistive MHD flows
KW - Transverse magnetic field
KW - Uniform regularity
KW - Vanishing viscosity limit
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U2 - 10.3934/cpaa.2021073
DO - 10.3934/cpaa.2021073
M3 - 21_Publication in refereed journal
VL - 20
SP - 2725
EP - 2750
JO - Communications on Pure and Applied Analysis
JF - Communications on Pure and Applied Analysis
SN - 1534-0392
IS - 7&8
ER -