Abstract
We consider steady flows of shear thinning fluids in bounded domains under the action of external forces and Dirichlet boundary conditions. For a power-law index q∈(2d∕(d+2),3d∕(d+2)], we construct weak solutions to the nonhomogeneous boundary value problem assuming that the boundary data is small enough. Moreover, under the restriction q∈((2d−1)∕d,2), d=2,3, and extra regularity for the boundary data, we construct weak solutions by extending the tangential part of the velocity at the boundary in such a way that it is possible to partially control the inertial term. This imposes restrictions only on the size of the normal component of the boundary data.
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