Appears in collections : Colloque Scientifique International Poincaré 100, Abel Prize

Fluid dynamics and Turbulence Theory where among lecture courses given by Poincare. If we add his lectures on the theory of vortices we can have a clear impression that fluid dynamics was among his favorite fields. Recently there appeared new results which allow one to say that fluid dynamics is under an intensive development. I have in mind a general tendency to construct new concrete classes of solutions which may haave applications in climate theory, physics of atmosphere and others. In particular I mean new progress in solutions of the Euler equations,the renormalization group method which was anticipated in some form by Poincare, various types of bifurcations of vortices, etc. These topics will be the main part of my presentation.