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Global free boundary problem for viscous non-homogeneous incompressible magnetohydrodynamics

Volume 535 / 2018

Piotr Kacprzyk Dissertationes Mathematicae 535 (2018), 59-101 MSC: Primary 35A01; Secondary 35Q30, 35R35, 76D05, 76W05. DOI: 10.4064/dm768-2-2018 Published online: 15 November 2018

Abstract

We consider the motion of viscous non-homogeneous incompresible magnetohydrodynamics in a domain bounded by a free surface. An electromagnetic field generated by some currents in the external domain keeps the magnetohydrodynamic flow in the bounded domain. On the free surface, transmission conditions for electromagnetic fields are imposed. The global-in-time existence of the solution is proved for small initial velocity and vanishing external force. The $L_2$ approach is used. This enables us to treat the transmission conditions.

Authors

  • Piotr KacprzykInstitute of Mathematics and Cryptology
    Cybernetics Faculty
    Military University of Technology
    Kaliskiego 2
    00-908 Warszawa, Poland
    e-mail

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