Almost global solutions of the free boundary problem for the equations of a magnetohydrodynamic incompressible fluid

Volume 31 / 2004

Piotr Kacprzyk Applicationes Mathematicae 31 (2004), 69-77 MSC: 35A05, 35R35, 76N10. DOI: 10.4064/am31-1-6

Abstract

Almost global in time existence of solutions for equations describing the motion of a magnetohydrodynamic incompressible fluid in a domain bounded by a free surfaced is proved. In the exterior domain we have an electromagnetic field which is generated by some currents which are located on a fixed boundary. We prove that a solution exists for $t\in (0,T)$, where $T>0$ is large if the data are small.

Authors

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

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