On the Existence, Uniqueness and Regularity of Solutions for a Class of MHD Equations of Non-Newtonian Type

Abstract

In this paper, we consider a steady MHD fluid model of non-Newtonian type in a smooth bounded domain Ω ∈ R 3 . Using the iterative method, under the condition that the external force is small in a suitable sense, we proved the existence of C 1,γ (Ω) × W 2,r (Ω) solutions of the systems for the exponent 1 < p < 2 and we show that this solution is unique in case 6 5 < p < 2. Moreover, we also proved the higher regularity properties of this solution.