Mathematical Foundation of Turbulent Viscous Flows: Lectures given at the C.I.M.E. Summer School held...

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Peter Constantin Marco Cannone

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...

Peter Constantin, Marco Cannone, Giovanni Gallavotti , Tetsuro Miyakawa

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English

Springer-Verlag Berlin and Heidelberg GmbH & Co. K
10 January 2006

Fluid mechanics; Flow, turbulence, rheology

Series: C.I.M.E. Foundation Subseries

Summary
Details

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.

By: Peter Constantin, Giovanni Gallavotti, Alexandre V. Kazhikhov
Edited by: Marco Cannone, Tetsuro Miyakawa
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Country of Publication: Germany
Volume: 1871
Dimensions: Height: 235mm, Width: 155mm, Spine: 15mm
Weight: 454g
ISBN: 9783540285861
ISBN 10: 3540285865
Series: C.I.M.E. Foundation Subseries
Pages: 264
Publication Date: 10 January 2006
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active