The decay rates of strong solutions for Navier-Stokes equations (Q1604252)

This paper deals with the existence and decay rate of global strong solutions in \(L^q\) for the Navier Stokes equations in \(\mathbb{R}^3\). The authors first construct approximate solutions through linearizing the Navier-Stokes equations. To this end they use directly the fundamental solution of heat equations in \(\mathbb{R}^3\) to obtain decay estimates of arbitrary order derivatives. Note that the estimate for the decay rate is optimal in the sense that it coincides with the decay rate of a solution to the heat equation.