Rigorous results in space-periodic two-dimensional turbulence

We survey the recent advance in the rigorous qualitative theory of the 2d stochastic Navier-Stokes system that are relevant to the description of turbulence in two-dimensional fluids. After discussing briefly the initial-boundary value problem and the associated Markov process, we formulate results on the existence, uniqueness and mixing of a stationary measure. We next turn to various consequences of these properties: strong law of large numbers, central limit theorem, and random attractors related to a unique stationary measure. We also discuss the Donsker-Varadhan and Freidlin-Wentzell type large deviations, as well as the inviscid limit and asymptotic results in 3d thin domains. We conclude with some open problems

Optimal Control of Coupled Systems of PDE

The Workshop Optimal Control of Coupled Systems of PDE was held from April 17th – April 23rd, 2005 in the Mathematisches Forschungsinstitut Oberwolfach. The scientific program covered various topics such as controllability, feedback control, optimality conditions,analysis and control of Navier-Stokes equations, model reduction of large systems, optimal shape design, and applications in crystal growth, chemical reactions and aviation