Large time regular solutions to the MHD equations in cylindrical domains

Tom 38 / 2011

Wisam Alame, Wojciech M. Zajączkowski Applicationes Mathematicae 38 (2011), 117-146 MSC: 35Q35, 35G20, 35G30, 76W05. DOI: 10.4064/am38-2-1


We prove the large time existence of solutions to the magnetohydrodynamics equations with slip boundary conditions in a cylindrical domain. Assuming smallness of the $L_2$-norms of the derivatives of the initial velocity and of the magnetic field with respect to the variable along the axis of the cylinder, we are able to obtain an estimate for the velocity and the magnetic field in $W_2^{2,1}$ without restriction on their magnitude. Then the existence follows from the Leray–Schauder fixed point theorem.


  • Wisam AlameFaculty of Mathematics and Information Sciences
    Warsaw University of Technology
    Pl. Politechniki 1
    00-661 Warszawa, Poland
  • Wojciech M. ZajączkowskiInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-956 Warszawa, Poland
    Institute of Mathematics and Cryptology
    Cybernetics Faculty
    Military University of Technology
    Kaliskiego 2
    00-908 Warszawa, Poland

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