Decay of solutions to a class of incompressible third grade fluid equations

Abstract

In this paper, we study the long time behavior of solutions to a class of the third grade fluid equations in R3. We first show that the solutions decay to zero if the initial data u0∈L2(R3). Then, applying Fourier splitting method and decay character r⁎, we establish the upper and lower bounds of time decay rate in L2-norm for the solutions.