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Large time regular solutions to the MHD equations in cylindrical domains

Tom 38 / 2011

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

Streszczenie

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.

Autorzy

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

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