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Weak Solutions to Unsteady and Steady Models of Conductive Magnetic Fluids

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Abstract

We study a nonlinear coupling system of partial differential equations describing the dynamic of a magnetic fluid with internal rotations. The present mathematical model generalizes those discussed previously in the literature since actually the fluid is electrically conducting inducing additional nonlinearities in the problem and the dynamics of the magnetic field is described by the quasi-static Maxwell equations instead of the usual magnetostatic ones. We prove existence of weak solutions with finite energy first for the unsteady problem then for the steady one.

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Authors and Affiliations

  1. DVRC, Léonard de Vinci Pôle Universitaire, 92916, Paris la Défense Cedex, France

    Kamel Hamdache

  2. Laboratoire AMNEDP, Faculté de Mathématiques, Université USTHB, Algiers, Algeria

    Djamila Hamroun

Authors
  1. Kamel Hamdache
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  2. Djamila Hamroun
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Correspondence to Djamila Hamroun.

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Hamdache, K., Hamroun, D. Weak Solutions to Unsteady and Steady Models of Conductive Magnetic Fluids. Appl Math Optim 81, 479–509 (2020). https://doi.org/10.1007/s00245-018-9505-x

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  • DOI: https://doi.org/10.1007/s00245-018-9505-x

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