On the decay of higher order derivatives of solutions to Ladyzhenskaya model for incompressible viscous flows

This article concerns large time behavior of Ladyzhenskaya model for incompressible viscous flows in R-3. Based on linear L-p-L-q estimates, the auxiliary decay properties of the solutions and generalized Gronwall type arguments, some optimal upper and lower bounds for the decay of higher order derivatives of solutions are derived without assuming any decay properties of solutions and using Fourier splitting technology.