Local existence of solutions of the free boundary problem for the equations of a magnetohydrodynamic incompressible fluid

Volume 30 / 2003

Piotr Kacprzyk Applicationes Mathematicae 30 (2003), 461-488 MSC: 35A05, 35R35, 76N10. DOI: 10.4064/am30-4-8


Local existence of solutions is proved for equations describing the motion of a magnetohydrodynamic incompressible fluid in a domain bounded by a free surface. In the exterior domain we have an electromagnetic field which is generated by some currents located on a fixed boundary. First by the Galerkin method and regularization techniques the existence of solutions of the linarized equations is proved; next by the method of successive aproximations the local existence is shown for the nonlinear problem.


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

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