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TitleAdvances 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 / edited by Josef Mรกlek, Jindล{153}ich Neฤ{141}as, Mirko Rokyta
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2000
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Descript IX, 236 p. online resource


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 adยญ 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 equaยญ 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 equaยญ and threeยญ tions for compressible fluids. The global (in time) analysis of two dimensional motions of compressible fluids were left open for many years


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

Mathematics Mathematical analysis Analysis (Mathematics) Integral equations Numerical analysis Physics Continuum physics Fluids Mathematics Analysis Classical Continuum Physics Integral Equations Numerical Analysis Theoretical Mathematical and Computational Physics Fluid- and Aerodynamics


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