Interior regularity to the steady incompressible shear thinning fluids with non-standard growth - Bae, Hyeong Ohk; So, Hyoungsuk; Youn, Yeonghun (Networks and Heterogeneous Media, 2018)
We consider weak solutions to the equations of stationary motion of a class of non-Newtonianfluids which includes the power law model. The power depends on the spatial variable, which is motivated by electrorheologicalfluids. We prove the existence of second order derivatives of weak solutions in the shear thinning cases.
Keywords: Interior regularities; Power-lawfluid; Regularity; Second order derivatives; Shear thinning fluids; Stationary motions; Strong solution; Variable exponents; Power-lawfluid; Regularity; Shear thinningfluid; Strong solution; Variable exponent space