This Research Note presents several contributions and mathematical studies in fluid mechanics, namely in non-Newtonian and viscoelastic fluids and on the Navier-Stokes equations in unbounded domains. It includes review of the mathematical analysis of incompressible and compressible flows and results in magnetohydrodynamic and electrohydrodynamic stability and thermoconvective flow of Boussinesq-Stefan type. These studies, along with brief communications on a variety of related topics comprise the proceedings of a summer course held in Lisbon, Portugal in 1991. Together they provide a set of comprehensive survey and advanced introduction to problems in fluid mechanics and partial differential equations.

This volume gathers most of the lectures and communications presented at the meeting t held in Bordeaux from the 27th to the 29 h of September and entitled "Far from equi librium : instabilities and structures". This meeting is part of a series of seve ral other interdisciplinary conferences such as Elmau 1972, London 1974, Dortmund 1976, Elmau 1977, Tokyo 1978. The old science classification scheme proposed by Auguste Comte tends to be eve ry day a bit more blurred out: one gives here, if needed, one additional illustra tion of this trend. The three key words "far from equilibrium", "instabilities" and "structures" best illustrate the new concepts which emerge from the description of the dynamics of various systems relevant to many different research areas. Laser emission, chemical reactions, fluid motions, exhibit very particular phenomena when, under appropriate external action,they occur far from equilibrium. These proceedings include the experimental description of such phenomena as well as theoretical at tempts in understanding them. Most of the topics investigated here belong to the domains of physics and chemistry but one should be careful not to underestimate the underlying potential biological interest. If the study of simple systems (e. g. , described by a few variables) has been qui te successful for several centuries, the recent bearing of our attention on complex systems constitutes a genuine epistemological breakthrough bridging the gap which used to exist between the sciences and the humanism.

Includes following subjects: Solution of equations in Rn, Finite difference methods, Finite element methods, Techniques of scientific computing, Optimization theory and systems science, Numerical methods for fluids, Numerical methods for solids, Specific applications

This volume contains the texts of selected lectures delivered at the "International Conference on Navier-Stokes Equations: Theory and Numerical Methods," held during 1997 in Varenna, Lecco (Italy). In recent years, the interest in mathematical theory of phenomena in fluid mechanics has increased, particularly from the point of view of numerical analysis. The book surveys recent developments in Navier-Stokes equations and their applications, and contains contributions from leading experts in the field. It will be a valuable resource for all researchers in fluid dynamics.

This volume contains 36 research papers written by prominent researchers. The papers are based on a large satellite conference on scientific computing held at the International Congress of Mathematics (ICM) in Xi'an, China. Topics covered include a variety of subjects in modern scientific computing and its applications, such as numerical discretization methods, linear solvers, parallel computing, high performance computing, and applications to solid and fluid mechanics, energy, environment, and semiconductors. The book will serve as an excellent reference work for graduate students and researchers working with scientific computing for problems in science and engineering.