Conservation laws arise from the modeling of physical processes through the following three steps: 1) The appropriate physical balance laws are derived for m-phy- t cal quantities, ul""' with u = (ul' ..., u ) and u(x, t) defined m for x = (xl""' ) E RN (N = 1,2, or 3), t > 0 and with the values m u(x, t) lying in an open subset, G, of R, the state space. The state space G arises because physical quantities such as the density or total energy should always be positive; thus the values of u are often con- strained to an open set G. 2) The flux functions appearing in these balance laws are...

This comprehensive introduction to the mathematical theory of vorticity and incompressible flow begins with the elementary introductory material and leads into current research topics. While the book centers on mathematical theory, many parts also showcase the interaction among rigorous mathematical theory, numerical, asymptotic, and qualitative simplified modeling, and physical phenomena. The first half forms an introductory graduate course on vorticity and incompressible flow. The second half comprises a modern applied mathematics graduate course on the weak solution theory for...

This IMA Volume in Mathematics and its Applications COMPUTATIONAL FLUID DYNAMICS AND REACTING GAS FLOWS is in part the proceedings of a workshop which was an integral part of the 1986-87 IMA program on SCIENTIFIC COMPUTATION. We are grateful to the Scientific Committee: Bjorn Engquist (Chairman), Roland Glowinski, Mitchell Luskin and Andrew Majda for planning and implementing an exciting and stimulating year-long program. We especially thank the Workshop Organizers, Bjorn Engquist, Mitchell Luskin and Andrew Majda, for organizing a workshop which brought together many of the leading...