By Marco Cannone (auth.), Josef Málek, Jindřich Nečas, Mirko Rokyta (eds.)
This e-book contains six survey contributions which are fascinated by a number of open difficulties of theoretical fluid mechanics either for incompressible and compressible fluids. the 1st article "Viscous flows in Besov areas" by means of M zone Cannone advert attire the matter of worldwide lifestyles of a uniquely outlined technique to the three-d Navier-Stokes equations for incompressible fluids. between others the next themes are intensively taken care of during this contribution: (i) the systematic description of the areas of preliminary stipulations for which there exists a special neighborhood (in time) resolution or a distinct international answer for small facts, (ii) the life of ahead self-similar suggestions, (iii) the relation of those effects to Leray's vulnerable ideas and backward self-similar strategies, (iv) the extension of the implications to additional nonlinear evolutionary difficulties. specific cognizance is paid to the serious areas which are invariant below the self-similar remodel. For small enough Reynolds numbers, the conditional balance within the feel of Lyapunov is additionally studied. the item is endowed through attention-grabbing own and ancient reviews and an exhaustive bibliography that provides the reader an entire photo approximately to be had literature. The papers "The dynamical procedure method of the Navier-Stokes equa tions for compressible fluids" via Eduard Feireisl, and "Asymptotic difficulties and compressible-incompressible limits" by means of Nader Masmoudi are dedicated to the worldwide (in time) homes of strategies to the Navier-Stokes equa and 3 tions for compressible fluids. the worldwide (in time) research of 2 dimensional motions of compressible fluids have been left open for plenty of years.
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Extra resources for Advances in Mathematical Fluid Mechanics: Lecture Notes of the Sixth International School Mathematical Theory in Fluid Mechanics, Paseky, Czech Republic, Sept. 19–26, 1999
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Advances in Mathematical Fluid Mechanics: Lecture Notes of the Sixth International School Mathematical Theory in Fluid Mechanics, Paseky, Czech Republic, Sept. 19–26, 1999 by Marco Cannone (auth.), Josef Málek, Jindřich Nečas, Mirko Rokyta (eds.)