This paper is supported by Guangzhou Natural Science Foundation (Grant No. 2024A04J4507), Natural Science Foundation of Guangdong Province (Grant No.2023A1515012044), and Bureau of Education in Guangdong Province (Grant No. 2025ZDZX4046).
References
[1] Kundu PK, Cohen IM. Fluid Mechanics. 3rd ed. Elsevier Academic Press; 2004. p. 737-8.
[2] Gilbert A. Dynamo Theory. In: Friedlander S, Serre D, editors. Handbook of Mathematical Fluid Dynamics. Vol. II. Elsevier; 2003. p. 355-441.
[3] Prandtl L. Uber Flussigkeitsbewegung bei Sehr Kleiner Reibung. In: Actes du 3eme Congres International des Mathematiciens; 1904; Heidelberg. Leipzig: Teubner; 1904. p. 484-91.
[4] Liu C, Xie F, Yang T. MHD Boundary Layers Theory in Sobolev Spaces without Monotonicity. I. Well-Posedness Theory. Commun Pure Appl Math. 2019;72(1):63-121.
[5] Gerard-Varet D, Prestipino M. Formal Derivation and Stability Analysis of Boundary Layer Models in MHD. Z Angew Math Phys. 2017;68(3):76.
[6] Chen D, Ren S, Wang Y, Zhang Z. Long Time Well-Posedness of the MHD Boundary Layer Equation in Sobolev Space. Anal Theory Appl. 2020;36(1):1-18.
[7] Wang S, Xin Z. Boundary Layer Problems in the Vanishing Viscosity-Diffusion Limits for the Incompressible MHD System. Acta Math Sin. 2017;47(10):1303-26.
[8] Wu Z, Wang S. Zero Viscosity and Diffusion Vanishing Limit of the Incompressible Magnetohydrodynamic System with Perfectly Conducting Wall. Nonlinear Anal Real World Appl. 2015;24:50-60.
[9] Liu C, Xie F, Yang T. Justification of Prandtl Ansatz for MHD Boundary Layer. SIAM J Math Anal. 2019;51(3):2748-91.
[10] Wang S, Wang N. The Boundary Layer Problem of MHD System with Noncharacteristic Perfect Conducting Wall. Appl Anal. 2019;98(3):516-35.
[11] Ding S, Lin Z, Xie F. Verification of Prandtl Boundary Layer Ansatz for Steady Electrically Conducting Fluids with a Moving Physical Boundary. SIAM J Math Anal. 2021;53(5):4997-5059.
[12] Liu CJ, Yang T, Zhang Z. Validity of Prandtl Expansions for Steady MHD in the Sobolev Framework. SIAM J Math Anal. 2023;55(3):2377-410.
[13] Ding S, Wang C. Validity of Prandtl Layer Expansions for Steady Magnetohydrodynamics over a RotatingDisk. J Math Phys. 2023;64(2):021510.
[14] Ding S, Ji Z, Lin Z. Global-in-x Stability of Prandtl Layer Expansions for Steady Magnetohydrodynamics Flows over a Moving Plate. J Differ Equ. 2024;411:119-203.
[15] Wang X. A Kato Type Theorem on Zero Viscosity Limit of Navier-Stokes Flows. Indiana Univ Math J. 2001;50:223-41.
[16] Mazzucato A, Michael T. Vanishing Viscosity Plane Parallel Channel Flow and Related Singular Perturbation Problems. Anal PDE. 2008;1(1):35-93.
[17] Mazzucato A, Niu D, Wang X. Boundary Layer Associated with a Class of 3D Nonlinear Plane Parallel Channel Flows. Indiana Univ Math J. 2011;60(4):1113-36.
[18] Han D, Mazzucato A, Niu D, Wang X. Boundary Layer for a Class of Nonlinear Pipe Flow. J Differ Equ. 2012;252(12):6387-413.
[19] Wu Z, Wang S. Viscosity vanishing limit of the nonlinear pipe magnetohydrodynamic flow with diffusion. Math Methods Appl Sci. 2019;42:161-74.
[20] Wu Z, Wang S. Diffusion Vanishing Limit of the Nonlinear Pipe Magnetohydrodynamic Flow with Fixed Viscosity. Acta Math Sci. 2018;38B(2):627-42.
[21] Wang N, Wang S. Vanishing Vertical Limit of the Incompressible Combined Viscosity and Magnetic Diffusion Magnetohydrodynamic System. Math Methods Appl Sci. 2018;41(13):5015-49.
[22] Ding S, Lin Z, Niu D. Stability of the Boundary Layer Expansion for the 3D Plane Parallel MHD Flow. J Math Phys. 2021;62:021510.