Existence of Strong Solutions for Incompressible Fluids with Shear Dependent Viscosities
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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].
Mathematics Subject Classification (2000).Primary 76A05 secondary 35K65, 35Q35, 35B65
Keywords.Non-Newtonian fluids shear dependent viscosity degenerate parabolic systems weak and strong solutions shifted N-functions
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