, Volume 12, Issue 1, pp 101-132
Date: 30 Sep 2008

Existence of Strong Solutions for Incompressible Fluids with Shear Dependent Viscosities

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Abstract.

Certain rheological behavior of non-Newtonian fluids in engineering sciences is often modeled by a power law ansatz with p ∈ (1, 2]. In the present paper the local in time existence of strong solutions is studied. The main result includes also the degenerate case (δ = 0) of the extra stress tensor and thus improves previous results of [L. Diening and M. Růžička, J. Math. Fluid Mech., 7 (2005), pp. 413–450].

Communicated by H. Beirão da Veiga