Partial Differential Equations in Fluid Dynamics

Isom Herron is a Professor of Mathematics at Rensselaer Polytechnic Institute. After completing his PhD at The Johns Hopkins University and a post-doctoral at the California Institute of Technology, he was in the Mathematics Department at Howard University for many years, and he has held visiting appointments at Northwestern University, University of Maryland, MIT, and Los Alamos National Laboratory. Professor Herron's research is in one of the richest areas of applied mathematics: the theory of the stability of fluid flows. Common applications are to phenomena in the atmosphere and the oceans, to problems of the motion of ships and aircraft, and to internal machinery. Modern approaches involve new techniques in operator theory, energy methods, and dynamical systems. His current research interests are in stability of rotating magneto-hydrodynamic flows and more complicated geophysical flows such as groundwater, for which mathematical models are still being developed. Michael R. Foster is an Adjunct Professor of Mathematics at Rensselaer Polytechnic Institute and was a Professor at The Ohio State University in the Department of Aerospace Engineering from 1970 until 2006. Professor Foster's specialty is theoretical fluid dynamics, generally using asymptotic methods in conjunction with some computation. He focused for many years on geophysical fluid dynamics, enjoying rich collaborations with numerous distinguished professors at Arizona State University and the University of Dundee, and more recently Manchester. Since that time, his research has been in three areas: directional solidification problems, particularly in Bridgman devices; mathematical models of dendritic crystal growth; and boundary layers in dilute suspensions, especially the singularities that arise in standard models.

1. Review of analytic function theory; 2. Special functions; 3. Eigenvalue problems and eigenfunction expansions; 4. Green's functions for boundary-value problems; 5. Laplace transform methods; 6. Fourier transform methods; 7. Particular physical problems; 8. Asymptotic expansions of integrals.