research partners    
Ph.D. students    
consortium members    

Piotr Gwiazda
Institute of Applied Mathematics and Mechanics
University of Warsaw
Banacha 2,
02-097 Warsaw
phone: +48 22 5544551
fax: +48 22 5544700

Non-Newtonian fluids with nonstandard rheology
Piotr Gwiazda (MIM University of Warsaw) and Eduard Feireisl (Institute of Mathematics of Academy of Sciences CR)
in collaboration with Sarka Necasowa (Institute of Mathematics of Academy of Sciences CR) and Agnieszka Swierczewska (MIM University of Warsaw)
The project is carried out by Aneta Wróblewska at University of Warsaw
Our interest is directed to non-Newtonian fluids of strongly inhomogeneous behaviour with a high ability of increasing their viscosity under different stimuli, like the shear rate, magnetic or electric field. There is a wide range of possible applications of such fluids in numerous branches of industry, military and natural science, which entitled the intense research in this direction in the last years. Probably the most impressive are gels used for individual body protection in sport and medical applications and even for military armour.

The aim of this project will be the mathematical analysis of equations of the fluid motion including heat-conductivity of the fluid (cf. [3]) and realistic boundary conditions (Navier boundary condition). The formulation of the problem is supposed to meet the modern framework of implicit constitutive relation [2]. Currently, the well-possedness results are established only for incompressible isothermal flow with Dirichlet boundary conditions [1]. Solving the challenging question of existence of solutions to the described problem opens the possibility of analysis of the following important issues: (1) interactions of rigid and elastic bodies with non-Newtonian fluids, (2) long-time behaviour in the case of periodic forcing and (3) problem of stabilization to equilibria. Analytical work will be handled with the help of Eduard Feiresl's and Sarka Necasova's experience in the field of heat conducting flows and Piotr Gwiazda's and Agnieszka Swierczewska's experience in the field of space-inhomogeneous and shear thinning/thickening fluids.

[1] P. Gwiazda and A. Swierczewska, {2008} Math. Mod. Meth. Appl. Sci., 18: 1073-1092.
[2] K.R. Rajagopal, (2006) J. Fluid Mech., 550: 243-249.
[3] E. Feireisl, (2004) Dynamics of viscous compressible fluids, Oxford Lecture Ser. Math. Appl., 26 Oxford.