EXISTENCE AND REGULARITY OF SOLUTIONS AND THE STABILITY OF THE REST STATE FOR FLUIDS WITH SHEAR DEPENDENT VISCOSITY

In this paper we clarify and discuss some subtle features concerning the non-Newtonian fluid models which were considered by Malek, Necas and Ruzicka.(19) We establish new results regarding the stability of the rest state of mechanically isolated hows of such non-Newtonian fluids for arbitrary initial disturbances. We also discuss some results concerning the existence and regularity of solutions for small data. These results are based on a new method, giving convergence almost everywhere of approximations of gradients from boundedness of fraction of the L(2)-norm of the second and first derivatives, developed by Necas to study existence of solutions (global in time) to a class of partial differential equations.