Minimax principle for magnetohydrodynamic channel flow
Abstract
A new technique is used to derive maximum and minimum principles for a problem treated by Sloan (1973). In the study of this problem, Sloan has derived a dual variational principle, which can be used to obtain sequences that converge to the exact solution. The problem is concerned with a viscous incompressible electrically conducting fluid which flows steadily in a rectangular channel with a uniform transverse magnetic field parallel to one pair of walls, opposite pairs of walls being either insulators or perfect conductors. The method used in the investigation represents a new way of treating dual variational principles. The method can be applied to a large class of linear boundary value problems.
 Publication:

Zeitschrift Angewandte Mathematik und Physik
 Pub Date:
 September 1976
 DOI:
 10.1007/BF01591173
 Bibcode:
 1976ZaMP...27..613B
 Keywords:

 Channel Flow;
 Magnetohydrodynamic Flow;
 Minimax Technique;
 Variational Principles;
 Viscous Flow;
 Boundary Value Problems;
 Fourier Series;
 Incompressible Flow;
 Steady Flow;
 Wall Flow;
 Plasma Physics