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On multiscale homogenization problems in boundary layer theory

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Abstract

This paper is concerned with the homogenization of the equations describing a magnetohydrodynamic boundary layer flow past a flat plate, the flow being subjected to velocities caused by injection and suction. The fluid is assumed incompressible, viscous and electrically conducting with a magnetic field applied transversally to the direction of the flow. The velocities of injection and suction and the applied magnetic field are represented by rapidly oscillating functions according to several scales. We derive the homogenized equations, prove convergence results and establish error estimates in a weighted Sobolev norm and in C 0-norm. We also examine the asymptotic behavior of the solutions of the equations governing a boundary layer flow past a rough plate with a locally periodic oscillating structure.

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Authors and Affiliations

  1. Laboratoire de Mathématiques, CNRS UMR 6620, Université Blaise Pascal (Clermont-Ferrand 2), 63177, Aubière cedex, France

    Youcef Amirat

  2. Department of Differential Equations, Faculty of Mechanics and Mathematics, Moscow Lomonosov State University, Moscow, 119991, Russia

    Gregory A. Chechkin & Maxim Romanov

  3. Narvik University College, HIN, 8505, Narvik, Norway

    Gregory A. Chechkin

Authors
  1. Youcef Amirat
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  2. Gregory A. Chechkin
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  3. Maxim Romanov
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Correspondence to Youcef Amirat.

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The work of the second and the third author was partially supported by RFBR (project 12-01-00214).

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Amirat, Y., Chechkin, G.A. & Romanov, M. On multiscale homogenization problems in boundary layer theory. Z. Angew. Math. Phys. 63, 475–502 (2012). https://doi.org/10.1007/s00033-011-0167-7

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  • DOI: https://doi.org/10.1007/s00033-011-0167-7

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