Local Well-posedness for Linearized Degenerate MHD Boundary Layer Equations in Analytic Setting

2019 ◽  
Vol 35 (8) ◽  
pp. 1402-1418
Author(s):  
Ya Jun Li ◽  
Wen Dong Wang
Keyword(s):  
Boundary Layer ◽  
Well Posedness ◽  
Boundary Layer Equations ◽  
Mhd Boundary Layer

scholarly journals Well-posedness in Sobolev spaces of the two-dimensional MHD boundary layer equations without viscosity

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Wei-Xi Li ◽  
Rui Xu
Keyword(s):  
Boundary Layer ◽  
Sobolev Spaces ◽  
Tangential Component ◽  
Well Posedness ◽  
Two Dimensional ◽  
Uniqueness Of Solutions ◽  
Layer System ◽  
Boundary Layer Equations ◽  
Mhd Boundary Layer ◽  
Liu Xie

<p style='text-indent:20px;'>We consider the two-dimensional MHD Boundary layer system without hydrodynamic viscosity, and establish the existence and uniqueness of solutions in Sobolev spaces under the assumption that the tangential component of magnetic fields dominates. This gives a complement to the previous works of Liu-Xie-Yang [Comm. Pure Appl. Math. 72 (2019)] and Liu-Wang-Xie-Yang [J. Funct. Anal. 279 (2020)], where the well-posedness theory was established for the MHD boundary layer systems with both viscosity and resistivity and with viscosity only, respectively. We use the pseudo-differential calculation, to overcome a new difficulty arising from the treatment of boundary integrals due to the absence of the diffusion property for the velocity.</p>

A Mathematical Study on Non-Linear MHD Boundary Layer Past a Porous Shrinking Sheet with Suction

2019 ◽  
Vol 2 (2) ◽  
pp. 32-48
Author(s):  
V. Ananthaswamy ◽  
K. Renganathan
Keyword(s):  
Boundary Layer ◽  
Homotopy Analysis Method ◽  
Dimensionless Temperature ◽  
Shrinking Sheet ◽  
Analysis Method ◽  
Approximate Analytical Expression ◽  
Boundary Layer Equations ◽  
Mhd Boundary Layer ◽  
Homotopy Analysis ◽  
Good Agreement

In this paper we discuss with magneto hydrodynamic viscous flow due to a shrinking sheet in the presence of suction. We also discuss two dimensional and axisymmetric shrinking for various cases. Using similarity transformation the governing boundary layer equations are converted into its dimensionless form. The transformed simultaneous ordinary differential equations are solved analytically by using Homotopy analysis method. The approximate analytical expression of the dimensionless velocity, dimensionless temperature and dimensionless concentration are derived using the Homotopy analysis method through the guessing solutions. Our analytical results are compared with the previous work and a good agreement is observed.

An Initial Value Method for the Solution of MHD Boundary-Layer Equations

1970 ◽  
Vol 21 (1) ◽  
pp. 91-99 ◽  
Author(s):  
T. Y. Na
Keyword(s):  
Boundary Layer ◽  
Iteration Process ◽  
Physical Parameters ◽  
Point Boundary ◽  
Initial Value ◽  
Linear Ordinary Differential Equations ◽  
Boundary Layer Equations ◽  
Mhd Boundary Layer ◽  
Layer Flow ◽  
Mhd Boundary Layer Flow

SummaryAn initial value method is introduced in this paper for the solution of the two-point non-linear ordinary differential equations resulting from an analysis of the MHD boundary-layer flow originally treated by Greenspan and Carrier. By using this method, the iteration process is eliminated. The method is seen to be applicable to the solution of similar two-point boundary value problems where certain physical parameters appear either in the differential equation or in the boundary conditions and solutions for a range of the parameter are sought.

scholarly journals Magnetohydrodynamic cross-field boundary layer flow

1982 ◽  
Vol 5 (2) ◽  
pp. 377-384 ◽  
Author(s):  
D. B. Ingham ◽  
L. T. Hildyard
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Asymptotic Solution ◽  
Boundary Layer Flow ◽  
Leading Edge ◽  
Field Boundary ◽  
Boundary Layer Equations ◽  
Mhd Boundary Layer ◽  
Blasius Boundary Layer ◽  
Layer Flow

The Blasius boundary layer on a flat plate in the presence of a constant ambient magnetic field is examined. A numerical integration of the MHD boundary layer equations from the leading edge is presented showing how the asymptotic solution described by Sears is approached.

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