Impartido por el Dr. James Dufty,(University of Florida)Resumen
Hydrodynamic equations describe the dynamics of fluids and are essential to a wide range of common phenomena from airplane design and weather prediction to the manufacture and transport of beverages. Where does this set of five partial differential equations come from? This question is addressed for simple gases based on the more fundamental mesoscopic description of kinetic theory. Given the physical basis for the kinetic equation, it becomes a problem in applied mathematics to explain the origin of the "contracted" description of hydrodynamics. The solution to this problem during the past century based on results of Hilbert, Weyl, and Rellich is briefly reviewed. Interest in these issues has revived in recent years due to attempts to develop a hydrodynamics for "granular fluids" (e.g.,the flow of sand, beans, rice). Some recent progress is reported.