KTH/SU Mathematics Colloquium
06-05-24
Tony Lelievre, CERMICS - ENPC
Numerical and mathematical analysis of micro-macro models for
polymeric fluids.
The modelling of polymeric fluids by kinetic equations raises
interesting and original mathematical and numerical questions, since
it implies the coupling of two different mathematical objects: partial
differential equations and stochastic differential equations. We will
introduce the models and present some theoretical existence
results. We will also introduce the numerical
methods used to discretize the coupled PDE-SDE system. A major part of
the talk will be about the longtime behaviour of such micro-macro
models, that can be explored either by stochastic methods (coupling
methods) or analytic methods (entropy methods). Entropy methods use
the Fokker-Planck formulation of the SDEs, so that the longtime
behaviour analysis gives the opportunity to discuss both formulations.