Abstract.
A rigorous mathematical analysis is given for a magnetohydrodynamic boundary layer problem, which arises in the study of self-similar solutions of the two-dimensional steady laminar boundary layer flow for an incompressible electrically conducting non-dilatable fluid (i.e., a Newtonian fluid or a pseudo-plastic one) along an isolated surface in the presence of an exterior magnetic field orthogonal to the flow. For this problem, only a normal solution has the physical meaning. The uniqueness, existence, and nonexistence results for normal solutions are established. Also the asymptotic behavior of the normal solution at the infinity is displayed.
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The project was supported by NCET of Xiamen University and NNSF of China (No. 10501037).
Received: January 10, 2007; revised: September 6, 2007, April 21, 2008
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Zhang, Z. Self-similar solutions of the magnetohydrodynamic boundary layer system for a non-dilatable fluid. Z. Angew. Math. Phys. 60, 621–639 (2009). https://doi.org/10.1007/s00033-008-7002-9
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DOI: https://doi.org/10.1007/s00033-008-7002-9