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

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

ISBN-10: 3540677860

ISBN-13: 9783540677864

ISBN-10: 3642573088

ISBN-13: 9783642573088

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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Indust. Appl. Math. 14 (2) (1997),169-197. 114. F. D. Thesis, ENS Cachan (1998). 115. H. Pecher: Self-similar and asymptotically self-similar solutions of nonlinear wave equations, Math. Ann. 316 (2000), no. 2, 259-281. Viscous Flows in Besov Spaces 33 116. F. D. Thesis, Ecole Poly technique, France (1996). 117. F. Planchon: Global strong solutions in Sobolev or Lebesgue spaces for the incompressible Navier-Stokes equations in IR3 , Ann. Inst. H. Poinc. 13 (1996), 319-336. 118. F. Planchon: Convergence de solutions des equations de Navier-Stokes vers des solutions auto-similaires, Expose n.

M. Ben-Artzi: Global solutions of two-dimensional Navier-Stokes and Euler equation, Arch. Rat. Mech. Anal. 128 (1994), 329-358. 12. O. V. Besov: Investigation of a family of functional spaces connected with embedding and extension theorems, Trudy Mat. Inst. Steklov 60 (1961) (in Russian). 13. H. A. Biagioni, L. Cadeddu and T. Gramchev: Semilinear parabolic equations with singular initial data in anisotropic weighted spaces, Diff. and Integral Equations 12 (1999), 613-636. 14. H. A. Biagioni and T.

G. Tian and Z. Xin: One-point singular solutions to the Navier-Stokes equations, Topol. Methods Nonlinear Anal. 11 (1) (1998), 135-145. 139. T. P. Tsai: On Leray's self-similar solutions of the Navier-Stokes equations satisfying local energy estimates, Arch. Rational Mech. Anal 143 (1) (1998), 29-51. Erratum, ibid. 147 (1999), 363. 140. S. Tourville: An analysis of Numerical Methods for Solving the two-dimensional Navier-Stokes Equations, Ph. D. Thesis, Washington University of St. Louis, MO (1998).

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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.)

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