Interior gradient estimate for steady flows of electrorheological fluids. (October 2020) - Sin, Cholmin
Abstract: In this paper, we consider the equations of stationary motion of electrorheological fluids in any dimension n ≥ 2 . We show that the first gradient of local solutions to the system has optimal L q -regularity with some q > 1 with respect to the one of the external force. This is achieved by comparison principle and a good λ -estimate.