Introduction:

The NavierStokes equations represent the fundamental equations of fluid dynamics. Recently researchers from many countries around the world have found important new results to the theory of these equations and their applications: Existence proofs for weak, or strong, or even analytical solutions to timedependent as well as for stationary boundary value problems of the fully nonlinear Navier Stokes equations or for the linear Stokes equations, considered with a wide variety of initial and boundary conditions, uniqueness classes in the frame of suitably adapted abstract spaces, questions of asymptotic behavior and stability of solutions, of maximum regularity, new proofs of the maximum modulus theorem, and convergence results with vanishing viscosity. A further important part of research is the interaction of fluid flow with moving bodies or particles, or with additional heat flow, leading to enlarged dynamical systems which combine the NavierStokes equations with another equation of evolution. The strong progress in the theory opens the way to efficient numerical schemes for problems in technology and medicine.
The aim of our special session will be to bring together leading researchers from all parts of the world and from the different working directions mentioned above, and to initiate exchange of ideas as well as future cooperation. 
