Abstract
This paper is concerned with non-stationary flows of shear-thinning fluids in a bounded two-dimensional \(\mathcal {C}^{2,1}\) domain. Assuming perfect slip boundary conditions, we provide a proof of the existence of a solution with the Hölder continuous velocity gradients and pressure under condition that a stress tensor satisfies power-law with growth \(p\in [5/3;2]\).
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