Large time regular solutions to the MHD equations in cylindrical domains

Wisam Alame, and Wojciech M. Zajączkowski. "Large time regular solutions to the MHD equations in cylindrical domains." Applicationes Mathematicae 38.2 (2011): 117-146. <http://eudml.org/doc/279937>.

@article{WisamAlame2011,
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 L₂-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 $W₂^\{2,1\}$ without restriction on their magnitude. Then the existence follows from the Leray-Schauder fixed point theorem.},
author = {Wisam Alame, Wojciech M. Zajączkowski},
journal = {Applicationes Mathematicae},
keywords = {incompressible magnetohydrodynamics; slip boundary conditions; large time existence; Leray-Schauder fixed point theorem},
language = {eng},
number = {2},
pages = {117-146},
title = {Large time regular solutions to the MHD equations in cylindrical domains},
url = {http://eudml.org/doc/279937},
volume = {38},
year = {2011},
}

TY - JOUR
AU - Wisam Alame
AU - Wojciech M. Zajączkowski
TI - Large time regular solutions to the MHD equations in cylindrical domains
JO - Applicationes Mathematicae
PY - 2011
VL - 38
IS - 2
SP - 117
EP - 146
AB - We prove the large time existence of solutions to the magnetohydrodynamics equations with slip boundary conditions in a cylindrical domain. Assuming smallness of the L₂-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 $W₂^{2,1}$ without restriction on their magnitude. Then the existence follows from the Leray-Schauder fixed point theorem.
LA - eng
KW - incompressible magnetohydrodynamics; slip boundary conditions; large time existence; Leray-Schauder fixed point theorem
UR - http://eudml.org/doc/279937
ER -