Our next MORE seminar meeting will take place on Monday (May 9, 2016) at 9:00 am in K6. Prof. Endre Süli (Univesity of Oxford) will present a lecture on Navier-Stokes-Fokker-Planck systems: modelling, analysis, computation. Please see the details below.
We shall survey recent results concerning the mathematical theory and numerical approximation of coupled macroscopic-microscopic bead-spring chain models that arise from the kinetic theory of dilute solutions of polymeric fluids with noninteracting polymer chains, involving the unsteady incompressible or compressible Navier-Stokes system in a bounded domain and a high-dimensional Fokker-Planck equation. The Fokker-Planck equation emerges from a system of (Ito) stochastic differential equations, which models the evolution of a vectorial stochastic process comprised by the centre-of-mass position vector and the orientation (or configuration) vectors of the polymer chain. We discuss the existence of large-data global-in-time weak solutions to the coupled Navier-Stokes-Fokker-Planck system. The numerical approximation of this high-dimensional coupled system is a formidable computational challenge, complicated by the fact that for practically relevant spring potentials the drift term in the Fokker-Planck equation is unbounded. The results presented are based on a series of papers with John W. Barrett (Imperial College London), Miroslav Bulicek and Josef Malek (Charles University, Prague), Eduard Feireisl (Institute of Mathematics of the Czech Academy of Sciences) and Yong Lu (Charles University, Prague).