Abstract: We considered the first boundary value problems for a class of steady NonNewtonian micropolar fluid equations in a smooth bounded domain Ω∈Rⁿ (n=2,3). Under the conditions that the vortex viscosity coefficient and a certain norm of the external force term were appropriately small, we proved the existence and uniqueness of strong solutions of the system of equations by using the fixed point theorem with index p>1.

Key words: non-Newtonian fluid, micropolar fluid, strong solution, existence and uniqueness