Editors:
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1871)
Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)
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Table of contents (5 chapters)
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Front Matter
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Back Matter
About this book
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.
Keywords
- Boltzmann equation
- Fourier analysis
- Navier-Stokes equation
- fluid mechanics
- partial differential equation
- partial differential equations
- rarefied gas flows
Bibliographic Information
Book Title: Mathematical Foundation of Turbulent Viscous Flows
Book Subtitle: Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 1-5, 2003
Editors: Marco Cannone, Tetsuro Miyakawa
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/b11545989
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2006
Softcover ISBN: 978-3-540-28586-1Published: 10 January 2006
eBook ISBN: 978-3-540-32454-6Published: 24 November 2005
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: IX, 264
Topics: Differential Equations