Download Advances in Mathematical Fluid Mechanics: Lecture Notes of by Marco Cannone (auth.), Josef Málek, Jindřich Nečas, Mirko PDF

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By Marco Cannone (auth.), Josef Málek, Jindřich Nečas, Mirko Rokyta (eds.)

This publication contains six survey contributions which are curious about numerous open difficulties of theoretical fluid mechanics either for incompressible and compressible fluids. the 1st article "Viscous flows in Besov areas" through M region Cannone advert­ clothes the matter of world lifestyles of a uniquely outlined technique to the 3-dimensional Navier-Stokes equations for incompressible fluids. between others the next issues are intensively handled during this contribution: (i) the systematic description of the areas of preliminary stipulations for which there exists a distinct neighborhood (in time) resolution or a distinct worldwide resolution for small facts, (ii) the life of ahead self-similar ideas, (iii) the relation of those effects to Leray's susceptible strategies and backward self-similar options, (iv) the extension of the consequences to additional nonlinear evolutionary difficulties. specific realization is paid to the serious areas which are invariant below the self-similar remodel. For small enough Reynolds numbers, the conditional balance within the experience of Lyapunov can also be studied. the thing is endowed by way of attention-grabbing own and historic reviews and an exhaustive bibliography that offers the reader a whole photo approximately to be had literature. The papers "The dynamical method 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) houses 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 lots of years.

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Read Online or Download Advances in Mathematical Fluid Mechanics: Lecture Notes of the Sixth International School Mathematical Theory in Fluid Mechanics, Paseky, Czech Republic, Sept. 19–26, 1999 PDF

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Extra info 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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Kato and G. Ponce: The Navier-Stokes equations with weak initial data, Int. Math. Res. Notes 10 (1994), 435-444. 75. T. Kawanago: Stability of global strong solutions of the Navier-Stokes equations, Nonlinear evolution equations and their applications, (Japanese) Surikaisekikenkyusho Kokyuroku 913 (1995), 141-147. 76. T. Kawanago: Stability estimate of strong solutions for the Navier-Stokes system and its applications, Electron. J. html) 15 (1998), 1-23. Viscous Flows in Besov Spaces 31 77. H. Koch and D.

Planchon: On the non stationary Navier-Stokes equations with an external force, Adv. in Diff. Eq. 4 (5) (1999), 697-730. 31. M. Cannone et F. Planchon: Fonctions de Lyapunov pour les equations de Navier-Stokes, Expose n. VIII, Seminaire X-EDP, Ecole Polytechnique (2000), 1-7. 32. M. Cannone and F. Planchon: More Lyapunov functions for the Navier-Stokes equations, submitted (2000). 33. M. Cannone, F. Planchon and M. E. Schonbek: Navier-Stokes equations in the half space, Comm. Part. Diff. Equat.

8. C. Bardos and S. Ukai: The classical incompressible Navier-Stokes limit ofthe Boltzmann equation, Math. Mod. Meth. Appl. Sc. 1 (2) (1991), 235-257. 9. O. A. Barraza: Self-similar solutions in weak LP spaces of the Navier-Stokes equations, Rev. Mat. Iberoamericana 12 (1996), 411-439. 10. O. A. Barraza: Regularity and stability for the solutions of the Navier-Stokes equations in Lorentz spaces, Nonlinear Anal. Ser. A: Theory Methods 35 (6) (1999), 747-764. 11. M. Ben-Artzi: Global solutions of two-dimensional Navier-Stokes and Euler equation, Arch.

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