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Existence and regularity of solutions and the stability of the rest state for fluids with shear dependent viscosity. (English) Zbl 0838.76005

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.

MSC:

76A05 Non-Newtonian fluids
35Q35 PDEs in connection with fluid mechanics
35B65 Smoothness and regularity of solutions to PDEs
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