Syllabus
J. Málek, K.R. Rajagopal: Mathematical issues concerning the Navier-Stokes equations and some of their generalizations. Handb. diff. equations. II, 371-459, 2005.
J. Málek, K. R. Rajagopal: Mathematical properties of the flows of incompressible fluids with pressure and shear rate dependent viscosities, Handb. Math. Fluid Dynamics IV, 2007.
P.L. Lions, N. Masmoudi: Global solutions for some Oldroyd models of non-Newtonian flows., Chinese Ann. Math. Ser. B 21 (2000), no. 2, 131--146. and other suitable research papers.
Annotation
Dealing with mechanical and thermal processes described by non-Newtonian fluid thermodynamics in terms of system of partial differential equations represing the balance equations for mass, linear and angular momentum, energy and entropy for each bulk of material, we present several approaches and mathematical tools that are successfully incorporated in order to eastablish large data mathematical properties of both steady and unsteady flows of such classes of fluids. Particularly, the questions of existence, uniqueness, regularity and large time behavior of weak solutions are studied.