An inequality for solutions of the Navier-Stokes equations in Rn

Abstract

We obtain a new inequality that holds for general Leray solutions of the incompressible Navier-Stokes equations in Rn (n <= 4). This recovers important results previously obtained by other authors regarding the time decay of solution derivatives (of arbitrary order).

This inequality was discovered by the authors in March 2016. A number of important results previously obtained by other authors regarding the large time decay of solution derivatives can now be seen as simple consequences of it (in the case n <= 4)