**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 $W^{{1,p}(x)}$ is a priori unknown. We investigate the question of the existence of a classical solution for the two dimensional periodic case. \noindent

This is a joint work with M. Bul\'{i}\v{c}ek and P. Kaplick\'y.

\vskip0.2cm \par 1 A. Abbatiello, M. Bul\'{i}\v{c}ek and P. Kaplick\'y, \textsl{On the existence of classical solution to the steady flows of generalized Newtonian fluid with concentration dependent power-law index}, forthcoming.

Mon 5 Feb, 16:45 - 17:20, Aula Dini

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