TY  - BOOK
AU  - Constantin,P.
AU  - Cannone,M.
AU  - Miyakawa,T.
ED  - Centro internazionale matematico estivo.
TI  - 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 
T2  - Lecture notes in mathematics,
SN  - 9783540324546
AV  - QA913 .M385 2006eb
U1  - 532/.58 22
PY  - 2006///
CY  - Berlin, New York
PB  - Springer
KW  - Turbulence
KW  - Mathematical models
KW  - Congresses
KW  - Viscous flow
KW  - Navier-Stokes equations
KW  - Mathematics
KW  - Modèles mathématiques
KW  - Congrès
KW  - Écoulement visqueux
KW  - Équations de Navier-Stokes
KW  - Mathématiques
KW  - mathematics
KW  - aat
KW  - applied mathematics
KW  - Turbulencia
KW  - Modelos matemáticos
KW  - Congresos
KW  - embne
KW  - fast
KW  - Reologie
KW  - gtt
KW  - Viscositeit
KW  - Partiële differentiaalvergelijkingen
KW  - Fourier-analyse
KW  - Congress
KW  - proceedings (reports)
KW  - Conference papers and proceedings
KW  - lcgft
KW  - Actes de congrès
KW  - rvmgf
N1  - Includes bibliographical references; Euler equations, Navier-Stokes equations and turbulence / Peter Constantin -- CKN theory of singularities of weak solutions of the Navier-Stokes equations / Giovanni Gallavotti -- Approximation of weak limits and related problems / Alexandre V. Kazhikhov -- Oscillating patterns in some nonlinear evolution equations / Yves Meyer -- Asymptotic analysis of fluid equations / Seiji Ukai; University staff and students only. Requires University Computer Account login off-campus
N2  - Annotation; Five well-known mathematicians 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. These questions are connected to the Caffarelli-Kohn-Nirenberg theory of singularities for the incompressible Navier-Stokes equations, that is explained in Gallavotti's lectures. Kazikhov introduces the theory of strong approximation of weak limits via the method of averaging, applied to Navier-Stokes equations. Y. Meyer focuses on several nonlinear evolution equations - in particular Navier-Stokes - and some related unexpected cancellation properties, either imposed on the initial condition, or satisfied by the solution itself, whenever it is localized in space or in time variable. Ukai presents the asymptotic analysis theory of fluid equations. He discusses the Cauchy-Kovalevskaya technique for the Boltzmann-Grad limit of the Newtonian equation, the multi-scale analysis, giving the compressible and incompressible limits of the Boltzmann equation, and the analysis of their initial layers
UR  - https://link-springer-com.libraryproxy.ist.ac.at/10.1007/b11545989
ER  -