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

Volume 31 / 2004

Piotr Kacprzyk Applicationes Mathematicae 31 (2004), 209-227 MSC: 35A05, 35R35, 76N10. DOI: 10.4064/am31-2-6


Local existence of solutions for the equations describing the motion of a magnetohydrodynamic compressible fluid in a domain bounded by a free surface is proved. 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 linearized equations is proved, next by the method of successive aproximations local existence to the nonlinear problem is shown.


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

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