Málek, J.; Rajagopal, K. R.; Růžička, M. Existence and regularity of solutions and the stability of the rest state for fluids with shear dependent viscosity. (English) Zbl 0838.76005 Math. Models Methods Appl. Sci. 5, No. 6, 789-812 (1995). We establish new results regarding the stability of the rest state of mechanically isolated flows of 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. Cited in 73 Documents MSC: 76A05 Non-Newtonian fluids 35Q35 PDEs in connection with fluid mechanics 35B65 Smoothness and regularity of solutions to PDEs Keywords:small data; convergence; approximations of gradients PDFBibTeX XMLCite \textit{J. Málek} et al., Math. Models Methods Appl. Sci. 5, No. 6, 789--812 (1995; Zbl 0838.76005) Full Text: DOI