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.
Acknowledgments. Bae was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2015R1D1A1A01057976 and 2016K2A9A2A 06005080) and Youn was supported by NRF (2015R1A4A1041675). The authors would like to thank referees for valuable comments and suggestions. The authors would like to express their sincere gratitudes Jihoon Ok for helpful discussions.
