The seminar will take place on Monday, March 5, 2018 at 9:00 am in K4. Anna Abbatiello will give a lecture “On the existence of classical solution to the steady flows of generalized Newtonian fluid with concentration dependent power-law index”.
Abstract: Steady flows of an incompressible synovial fluid are described by a coupled system, consisting of the generalized Navier – Stokes equations and convection – diffusion equation with diffusivity dependent on the concentration and the shear rate. Cauchy stress behaves like power-law fluid with the exponent depending on the concentration. It makes the problem much more difficult than the standard model for power-law fluid in the analysis of the system of PDEs, since the variable exponent space W1,p(x) is a priori unknown. We investigate the question of the existence of a classical solution for the two dimensional periodic case.
This is a joint work with M. Bulíček and P. Kaplický.
 A. Abbatiello, M. Bulíček and P. Kaplický, On the existence of classical solution to the steady flows of generalized Newtonian fluid with concentration dependent power-law index, forthcoming.