Large time regular solutions to the MHD equations in cylindrical domains
Volume 38 / 2011
Applicationes Mathematicae 38 (2011), 117-146
MSC: 35Q35, 35G20, 35G30, 76W05.
DOI: 10.4064/am38-2-1
Abstract
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.
