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An algebraic upper bound for the decay rate of solutions to the Navier-Stokesand Navier-Stokes-Coriolis equations in the critical space $\dot{H}^{\frac{1}{2}} (\mathbb{R} ^3)$ is derived using the Fourier Splitting Method.Estimates are framed in terms of the decay character of initial data, leadingto solutions with algebraic decay and showing in detail the roles played by thelinear and nonlinear parts.

Algebraic decay rates for 3D Navier-Stokes and Navier-Stokes-Coriolis equations in $ \dot{H}^{\frac{1}{2}}$