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.

[1] 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.