This award will support collaborative research in applied and computational mathematics between two groups of U.S. and French scientists, based at the University of Indiana at Bloomington and the French National Institute for Information Science and Automation (INRIA). The U.S. group will be led by Professor David Hoff; on the French side the project will be led by Dr. Bernard Larrouturou, INRIA, Sophia-Antipolis and Dr. Roger Temam, Laboratoire d'Analyse Numerique, University of Paris-South. The research will focus on a number of problems concerning reacting and nonreacting fluid flows. The project is subdivided into the following areas: 1. Navier-Stokes equations and turbulence 2. Numerical methods for reaction - diffusion systems and combustion problems 3. Reacting and nonreacting compressible flows 4. Flows of collisionless plasmas and the Vlasov-Maxwell Equations This research joins two groups of outstanding U.S. and French applied mathematicians. INRIA is widely recognized for its concentration of expertise in computer research, automation, mathematics and scientific computing; it provides an excellent combination of fundamental research with industrial collaboration in these areas. This award will allow fruitful collaboration to continue in the important area of fluid mechanics and combustion theory.