Weak solutions to stationary motions of shear thinning fluids with nonhomogeneous Dirichlet boundary conditions. (July 2021) - Elshehabey, Hillal M.; Silvestre, Ana L.
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 ∈ ( 2 d ∕ ( d + 2 ), 3 d ∕ ( 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 ∈ ( ( 2 d − 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.