Upper and lower bounds of time decay rate of solutions to a class of incompressible third grade fluid equations

This paper discusses the large time behaviors of solutions for a class of incompressible third grade fluid equations in R3R3. Using the Fourier splitting method of Schonbek, the authors prove the upper and lower bounds of the time decay rate in L2L2 for the weak solutions. The upper and lower bounds of decay rate are optimal in the sense that they coincide with the upper and lower bounds of the decay rate of solutions to the heat equation.