Existence and asymptotic behavior for an incompressible Newtonian flow with intrinsic degree of freedom

We consider the Cauchy problem of a mathematical model for an incompressible, homogeneous, Newtonian fluid taking into account internal degrees of freedom. We first show that there exists a unique global strong solution when the given initial data are small in some sense. Then, we deduce the optimal decay rates for velocity vector in L² ? norm and L^p ? norm for p > n. These decay estimates depend only on the spatial dimension and the decay properties of the heat solution with the same data. Copyright © 2013 John Wiley & Sons, Ltd.