We investigate a problem for a model of a non-Newtonian micropolar fluid coupled system. The problem has been considered in a bounded, smooth domain ofR3with Dirichlet boundary conditions. The operator stress tensor is given byτ(e(u))=[(ν+ν0M(|e(u)|2))e(u)]. To prove the existence of weak solutions we use the method of Faedo-Galerkin and compactness arguments. Uniqueness and periodicity of solutions are also considered.
In this paper, we investigate the existence and uniqueness of a solution for differential equations of the carrier type on lateral boundary † of the cylinder Q, cf. (1). The main point is to transform this initial value problem into a differential operator equation of the type u 00 C M ÂZ cf. (6). The operator A is defined in Section 2, and it acts in Sobolev spaces on , boundary of . The initial value problem (6) is investigated in Section 3 by the method of Faedo-Galerkin. Thus, we obtain the existence of a weak solution for (6), and in Section 4, we prove its uniqueness.Ã Au Cˇu 0ˇ u 0 D f , and we can apply the usual methodology for the initial value problem (6).
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