The authors consider an incompressible micropolar fluid system. This is a kind of non Newtonian fluid, and is a model of the suspensions, animal blood, liquid crystals which cannot be characterized appropriately by the Navier-Stokes system. It is described by the fluid velocity , the velocity of rotation of particles , and the pressure in the following form:
They assume that the initial values belong to the Besov space for some with small norms (this type of Besov space is called critical). They prove the existence of the solution in . They also prove the uniqueness under an additional assumption. For this purpose they consider an associated linear system
and study the action of its Green matrix.
One can apply thier result directly to an incompressible Navier-Stokes equation, by setting .