L2 decay of solutions for 2-D isotrophic non-Newtonian flows with partial dissipation

This paper is concerned with the L
²
decay of weak solutions of the isotrophic non-Newtonian flows with partial dissipation in whole space R
²
. By using the energy methods and modified Fourier splitting methods, we proved the optimal time decay rates of weak solutions for the system as ||u|| L
²
(R
²
) ≤ C(1 +t)
^-1/2
.