Magnetohydrodynamics (or MHD) is the theory of the macroscopic interaction of electrically conducting fluids with a magnetic field. It is of importance in connection with many engineering problems, such as sustained plasma confinement for controlled thermonuclear fusion, liquid-metal cooling of nuclear reactors, and electromagnetic casting of metals. It also finds applications in geophysics and astronomy, where one prominent example is the so-called dynamo problem, that is, the question of the origin of the Earth's magnetic field in its liquid metal core.
Due to their practical relevance, MHD flow problems have long been the subject of intense cross-disciplinary research, but except for relatively simple special cases, the rigorous mathematical and numerical analysis of such problems is largely terra incognita. The authors have recently developed a novel approach to an important class of MHD flow problems that circumvents some intrinsic difficulties of traditional analyses. The objective of the proposed research is to further pursue this approach in order to design qualitative and quantitative methods for the mathematically rigorous and computationally efficient solution of MHD flow problems in physically realistic situations.