By Josef Malek,Jindrich Necas,Mirko Rokyta

This e-book contains six survey contributions which are concerned about numerous 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 clothes the matter of world life of a uniquely outlined approach to the third-dimensional Navier-Stokes equations for incompressible fluids. between others the next issues 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 different worldwide resolution for small information, (ii) the lifestyles of ahead self-similar strategies, (iii) the relation of those effects to Leray's vulnerable strategies and backward self-similar suggestions, (iv) the extension of the implications to additional nonlinear evolutionary difficulties. specific cognizance is paid to the severe areas which are invariant below the self-similar rework. For small enough Reynolds numbers, the conditional balance within the feel of Lyapunov can be studied. the thing is endowed via attention-grabbing own and ancient reviews and an exhaustive bibliography that offers the reader a whole photograph approximately to be had literature. The papers "The dynamical approach method of the Navier-Stokes equa­ tions for compressible fluids" by way of Eduard Feireisl, and "Asymptotic difficulties and compressible-incompressible limits" by way of Nader Masmoudi are dedicated to the worldwide (in time) houses of options 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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