Lecture Notes of the Sixth International School Mathematical Theory in Fluid Mechanics, Paseky, Czech Republic, Sept. 19-26, 1999
Buch, Englisch, 236 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 365 g
ISBN: 978-3-540-67786-4
Verlag: Springer Berlin Heidelberg
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
- Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Strömungslehre
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
- Naturwissenschaften Physik Mechanik Kontinuumsmechanik, Strömungslehre
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen
- Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
Weitere Infos & Material
Viscous Flows in Besov Spaces.- The Dynamical Systems Approach to the Navier-Strokes Equations of Compressible Fluids.- Adaptive Wavelet Solvers for the Unsteady Incompressible navier-Strokes Equations.- Asymptotic Problems and Compressible-Incompressible Limit.- Weighted Spaces with Detached Asymptotic in Application to the Navier-Strokes Equations.- On the Mathematical Theory of Fluid Dynamic Limits to Conservation Laws.
