L2decay of solutions for 2-D isotrophic non-Newtonian flows with partial dissipation

Abstract

This paper is concerned with the L2 decay of weak solutions of the isotrophic non-Newtonian flows with partial dissipation in whole space R2. 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‖ L2(R2) ≤ C(1 +t)−1/2.