On the existence of unique global-in-time solutions and temporal decay rates of solutions to some non-Newtonian incompressible fluids

In this paper, we deal with a class of incompressible non-Newtonian fluids. We first give some conditions to the viscous part of the stress tensor to set our model. We then show that there exists a unique regular solution globally in time if u0 is an element of L2B</mml:mover>infinity ,11 and is sufficiently small in B<mml:mo></mml:mover>infinity <mml:mo>,11. We finally derive temporal decay rates of the solution which are consistent with the decay rates of the linear part of our model.