By Marco Cannone (auth.), Josef Málek, Jindřich Nečas, Mirko Rokyta (eds.)
This booklet includes six survey contributions which are fascinated about a number of open difficulties of theoretical fluid mechanics either for incompressible and compressible fluids. the 1st article "Viscous flows in Besov areas" through M quarter Cannone advert attire the matter of world life of a uniquely outlined approach to the third-dimensional Navier-Stokes equations for incompressible fluids. between others the next subject matters are intensively handled during this contribution: (i) the systematic description of the areas of preliminary stipulations for which there exists a special neighborhood (in time) answer or a different international resolution for small facts, (ii) the life of ahead self-similar suggestions, (iii) the relation of those effects to Leray's vulnerable recommendations and backward self-similar options, (iv) the extension of the consequences to extra nonlinear evolutionary difficulties. specific realization is paid to the serious areas which are invariant lower than the self-similar remodel. For small enough Reynolds numbers, the conditional balance within the experience of Lyapunov is usually studied. the object is endowed via attention-grabbing own and ancient reviews and an exhaustive bibliography that offers the reader an entire photo approximately to be had literature. The papers "The dynamical process method of the Navier-Stokes equa tions for compressible fluids" by means of Eduard Feireisl, and "Asymptotic difficulties and compressible-incompressible limits" through 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 lots of years.
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Additional 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
Cannone and F. Planchon: Self-similar solutions of the Navier-Stokes equations in IR3 , Comm. Part. Diff. Eq. 21 (1996), 179-193. 28. M. Cannone and F. Planchon: On the regularity of the bilinear term for solutions of the incompressible Navier-Stokes equations in IR3 , Rev. Mat. Iberoamericana (to appear) (2000). 29. M. Cannone and F. Planchon: Maximal function inequalities and NavierStokes equations, Investigations on the structure of solutions to partial differential equations (Japanese) (Kyoto, 1997).
56. G. Furioli: Applications de l'analyse harmonique reelle a. D. Thesis, UniversiM d'Orsay (1999). 30 Marco Cannone 57. G. Furioli: Solutions auto-similaires pour les equations de Schrodinger non lineaires, en preparation (1999). 58. G. -G. Lemarie-Rieusset et E. Terraneo: Sur l'unicite dans L 3(JR3) des solutions mild des equations de Navier-Stokes, C. R. Acad. Sci. Paris Ser. I Math. 325 (12) (1997), 1253-1256. 59. G. -G. Lemarie-Rieusset et E. Terraneo: Unicite dans L 3(JR3) et d'autres espaces fonctionnels limites pour Navier-Stokes, Rev.
Y. Le Jan et A. S. Sznitman: Cascades aleatoires et equations de NavierStokes, C. R. Acad. Sci. Paris 324 (7) (1997), 823-826. 89. Y. Le Jan and A. S. Sznitman: Stochastic cascades and 3-dimensional NavierStokes equations, Probab. Theory Related Fields 109 (3) (1997), 343-366. 90. -G. Lemarie-Rieusset: Some remarks on the Navier-Stokes equations in R3 , J. Math. Phys 39 (8) (1998), 4108-4118. 91. -G. Lemarie-Rieusset: Solutions faibles d'energie infinie pour les equations de Navier-Stokes dans R3 , C.
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.)