This book presents recent approaches to the phenomenon of turbulence in fluid flows by looking at the dynamical properties of the solutions of the Navier-Stokes equations. The variety of approaches and the technological implications of the basic issue make this book useful for applied mathematicians and engineers alike.

Inhalt
Application of an approximate R-N-G theory, to a model for turbulent transport, with exact renormalization.- Weak and strong turbulence in the complex Ginzburg Landau equation.- Symmetries, heteroclinic cycles and intermittency in fluid flow.- Finite-dimensional description of doubly diffusive convection.- Dynamical stochastic modeling of turbulence.- On a new type of turbulence for incompressible magnetohydrodynamics.- Loss of stability of the globally unique steady-state equilibrium and the bifurcation of closed orbits in a class of Navier-Stokes type dynamical systems.- Turbulent bursts, inertial sets and symmetry-breaking homoclinic cycles in periodic Navier-Stokes flows.- Navier-Stokes equations in thin 3D domains III: Existence of a global attractor.- An optimality condition for approximate inertial manifolds.- Some recent results on infinite dimensional dynamical systems.