Research On The Well-posedness Of Solutions For A Class Of Non-newtonian Micropolar Fluid Equations

In this paper,we mainly study the first initial and boundary value problems of the following non-Newtonian Micropolar Fluid Equations(?) Where(?)and it is a smooth and bounded domain.The function u denotes the velocity of the fluids;Du=1/2(?u+?Tu)denotes the strain rate tensor;w denotes the angular velocity;Du denotes the pressure of the fluids;f and g denote the given external force;? denotes the extra stress tensor,in this article we take the following two different forms,namely:?1=(Du)=2?(1+|Du|2)p-2/2 Du and?2(Du)=2?(1+|Du|)p-2 Du with p>1;? denotes the viscosity and ?r denotes the vortex viscosity,with ? and ?r are positive constants.For the above models,we use the linearization method and the fixed point theorem method to overcome the difficulties caused by the strong nonlinearity and strong coupling of the equations,and proved the existence and uniqueness of the strong solutions of the equations under the conditions that a certain norm of the external force term is suitably small.