Mathematical Foundation of Turbulent Viscous Flows : Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 1-5, 2003

Five leading specialists reflect on different and complementary approaches to fundamental questions in the study of the Fluid Mechanics and Gas Dynamics equations. Constantin presents the Euler equations of ideal incompressible fluids and discusses the blow-up problem for the Navier-Stokes equations of viscous fluids, describing some of the major mathematical questions of turbulence theory.