Series 
Lecture notes in mathematics, 00758434 ; 1871 

Lecture notes in mathematics (SpringerVerlag) ;
1871.

Subject 
Turbulence  Mathematical models  Congresses.


Viscous flow  Congresses.


NavierStokes equations  Congresses.

Alt Name 
Constantin, P. (Peter), 1951


Cannone, M. (Marco)


Miyakawa, T. (Tetsuro)


Centro internazionale matematico estivo.

Description 
1 online resource (ix, 252 pages) : illustrations. 

polychrome rdacc 
Bibliography Note 
Includes bibliographical references. 
Summary 
Annotation Five wellknown 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 blowup problem for the NavierStokes equations of viscous fluids, describing some of the major mathematical questions of turbulence theory. These questions are connected to the CaffarelliKohnNirenberg theory of singularities for the incompressible NavierStokes 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 NavierStokes equations. Y. Meyer focuses on several nonlinear evolution equations  in particular NavierStokes  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 CauchyKovalevskaya technique for the BoltzmannGrad limit of the Newtonian equation, the multiscale analysis, giving the compressible and incompressible limits of the Boltzmann equation, and the analysis of their initial layers. 
Contents 
Euler equations, NavierStokes equations and turbulence / Peter Constantin  CKN theory of singularities of weak solutions of the NavierStokes 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. 
Note 
Print version record. 
ISBN 
9783540324546 

3540324542 

9783540285861 (hardcover ; alk. paper) 

3540285865 (hardcover ; alk. paper) 
ISBN/ISSN 
10.1007/b11545989 
OCLC # 
262681828 
Link 
Springer ebooks 
Additional Format 
Print version: Mathematical foundation of turbulent viscous flows. Berlin ; New York : Springer, 2006 3540285865 (DLC) 2005936391 (OCoLC)63177840 
