Abstract
We investigate the steady flow of a shear thickening generalized Newtonian fluid under homogeneous boundary conditions on a domain in \({\mathbb{R}^{2}}\). We assume that the stress tensor is generated by a potential of the form \({H = h (|\varepsilon (u)|)}\), \({\varepsilon (u)}\) denoting the symmetric part of the velocity gradient. We prove the existence of strong solutions for a large class of functions h having the property that h′ (t)/t increases (shear thickening case).
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Communicated by H. Beirao da Veiga
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Fuchs, M. Stationary Flows of Shear Thickening Fluids in 2D . J. Math. Fluid Mech. 14, 43–54 (2012). https://doi.org/10.1007/s00021-010-0044-8
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DOI: https://doi.org/10.1007/s00021-010-0044-8