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On a class of fluids grade 3. (English) Zbl 0887.76007
Summary: We consider a class of a non-Newtonian fluids of grade 3. We give existence and uniqueness theorems for the two- and three-dimensional cases. These solutions are local ones. In the two-dimensional case, we show that for suitable data the solution can be defined globally. The proof of the main results are based on Galerkin method by using a special basis in an appropriate functional space.

MSC:
76A05 Non-Newtonian fluids
35Q35 PDEs in connection with fluid mechanics
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