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

Constantin presents the Euler equations of ideal incompressible fluids and the blow-up problem for the Navier-Stokes equations of viscous fluids, describing major mathematical questions of turbulence theory. These are connected to the Caffarelli-Kohn-Nirenberg theory of singularities for the incompressible Navier-Stokes equations, explained in Gallavotti's lectures. Kazhikhov introduces the theory of strong approximation of weak limits via the method of averaging, applied to Navier-Stokes equations. Y. Meyer focuses on nonlinear evolution equations and related unexpected cancellation properties, either imposed on the initial condition, or satisfied by the solution itself, localized in space or in time variable. Ukai discusses the asymptotic analysis theory of fluid equations, the Cauchy-Kovalevskaya technique for the Boltzmann-Grad limit of the Newtonian equation, the multi-scale analysis, giving compressible and incompressible limits of the Boltzmann equation, and the analysis of their initial layers.

Summary

Constantin
presents the Euler equations of ideal incompressible fluids and the blow-up problem for the Navier-Stokes equations of viscous fluids, describing major mathematical questions of turbulence theory. These are connected to the Caffarelli-Kohn-Nirenberg theory of singularities for the incompressible Navier-Stokes equations, explained in
Gallavotti
's lectures.
Kazhikhov
introduces the theory of strong approximation of weak limits via the method of averaging, applied to Navier-Stokes equations.
Y. Meyer
focuses on nonlinear evolution equations and related unexpected cancellation properties, either imposed on the initial condition, or satisfied by the solution itself, localized in space or in time variable.
Ukai
discusses the asymptotic analysis theory of fluid equations, the Cauchy-Kovalevskaya technique for the Boltzmann-Grad limit of the Newtonian equation, the multi-scale analysis, giving compressible and incompressible limits of the Boltzmann equation, and the analysis of their initial layers.

Product details

• Authors: Peter Constantin, Giovanni Gallavotti, Alexander V. Kazhikov, P. Constantin, Yves Meyer, Alexandre V. Kazhikhov, Seiji Ukai
• Assisted by: Marco Cannone (Editor), Tetsuro Miyakawa (Editor)
• Publisher: Springer, Berlin
• Content: Book
• Product form: Paperback / Softback
• Publication date: 14.04.2009
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Analysis
• EAN: 9783540285861
• ISBN: 978-3-540-28586-1
• Pages: 264
• Illustrations: IX, 264 p.
• Dimensions (packing): 15.7 x 1.6 x 23.5 cm
• Weight (packing): 426 g
• Series: Lecture Notes in Mathematics > 1871, Lecture Notes in Mathematics / Fondazione C.I.M.E., Firenze > Vol.1871, C.I.M.E. Foundation Subseries, Fondazione C.I.M.E., Firenze, Lecture Notes in Mathematics, C.I.M.E. Foundation Subseries
• Subjects: C, Mathematics and Statistics, Partial Differential Equations, Differential equations, Partial differential equation, rarefied gas flows