Advances in Mathematical Fluid Mechanics [electronic resource] : Lecture Notes of the Sixth International School Mathematical Theory in Fluid Mechanics, Paseky, Czech Republic, Sept. 19–26, 1999 /

This book consists of six survey contributions that are focused on several open problems of theoretical fluid mechanics both for incompressible and compressible fluids. The first article "Viscous flows in Besov spaces" by M area Cannone ad­ dresses the problem of global existence of a uniquely defined solution to the three-dimensional Navier-Stokes equations for incompressible fluids. Among others the following topics are intensively treated in this contribution: (i) the systematic description of the spaces of initial conditions for which there exists a unique local (in time) solution or a unique global solution for small data, (ii) the existence of forward self-similar solutions, (iii) the relation of these results to Leray's weak solutions and backward self-similar solutions, (iv) the extension of the results to further nonlinear evolutionary problems. Particular attention is paid to the critical spaces that are invariant under the self-similar transform. For sufficiently small Reynolds numbers, the conditional stability in the sense of Lyapunov is also studied. The article is endowed by interesting personal and historical comments and an exhaustive bibliography that gives the reader a complete picture about available literature. The papers "The dynamical system approach to the Navier-Stokes equa­ tions for compressible fluids" by Eduard Feireisl, and "Asymptotic problems and compressible-incompressible limits" by Nader Masmoudi are devoted to the global (in time) properties of solutions to the Navier-Stokes equa­ and three­ tions for compressible fluids. The global (in time) analysis of two dimensional motions of compressible fluids were left open for many years.

Bibliographic Details

Main Authors:	Málek, Josef. editor., Nečas, Jindřich. editor., Rokyta, Mirko. editor., SpringerLink (Online service)
Format:	Texto biblioteca
Language:	eng
Published:	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2000
Subjects:	Mathematics., Mathematical analysis., Analysis (Mathematics)., Integral equations., Numerical analysis., Physics., Continuum physics., Fluids., Analysis., Classical Continuum Physics., Integral Equations., Numerical Analysis., Theoretical, Mathematical and Computational Physics., Fluid- and Aerodynamics.,
Online Access:	http://dx.doi.org/10.1007/978-3-642-57308-8
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