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
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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
（Lecture notes in mathematics, 1871）
Springer, c2006
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Mathematical foundation of turbulent viscous flows : Martina Franca, Italy 2003
Available at / 64 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Etchujima library, Tokyo University of Marine Science and Technology自然
: pbk410.8/L 1/1871206289
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
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Includes bibliographical references
Description and Table of Contents
Description
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.
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