Dear Firedrake, There are two (quite mathematical) FEM talks in the Applied PDEs seminar next week. all the best --cjc Applied PDEs seminar Two talks: Endre Suli and Adrien Blanchet Date: 13 Nov 2013 Time: 16:00 - 18:00 Venue: Clore Lecture Theatre (Huxley Building Entrance Level 2) Campus: South Kensington Campus<http://www3.imperial.ac.uk/campusinfo/southkensington> Speaker: Dr Adrien Blanchet, Université Toulouse 1 Capitole Prof Endre Suli, Oxford Audience: Open to all Event type: Seminar Contact: Jose Carrillo de la Plata<mailto:carrillo@imperial.ac.uk>, Yanghong Huang<mailto:yanghong.huang@imperial.ac.uk> Endre Suli: Existence of global weak solutions to Navier-Stokes-Fokker-Planck systems Clore LT 16:00-17:00 The lecture will survey recent developments concerning the existence of global-in-time weak solutions to a general class of coupled microscopic-macroscopic bead-spring chain models that arise in the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The class of models involves the unsteady incompressible Navier-Stokes equations in a bounded domain for the velocity and the pressure of the fluid, with an elastic extra-stress tensor appearing on the right-hand side of the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is defined by the Kramers expression through the associated probability density function that satisfies a Fokker-Planck type parabolic equation, a crucial feature of which is the presence of a centre-of-mass diffusion term. The proof of a existence of global weak solutions is based on a combination of entropy estimates and weak compactness arguments. The lecture is based on a series of recent papers with John W. Barrett (Imperial College London). Adrien Blanchet: A gradient flow approach to the Keller-Segel systems. Clore LT 17:00-18:00 This talk is dedicated to recent results on the Keller-Segel model in 2d, and on its variants in higher dimensions where the diffusion is of critical porous medium type. These models have a critical mass $M_c$ such that the solutions exist globally in time if the mass is less than $M_c$ and above which there are solutions which blowup in finite time. The main tools, in particular the free energy and the Jordan-Kinderlherer-Otto's minimising scheme in the Monge-Kantorovich metric, and the idea of the methods are set out.