Some remarks on the regularity time of Leray solutions to the Navier-Stokes equations
arXiv:1706.10173
Abstract
In this small note we strengthen the classic result about the regularity time t* of arbitrary Leray solutions to the (incompressible) Navier-Stokes equations in Rn (n = 3, 4), which have the form: t* <= K_{3} nu^{-5} || u(.,0) ||_{L2}^{4} if n = 3, and t* <= K_{4} nu^{-3} || u(.,0) ||_{L2}^{2} if n = 4 (in particular, by reducing the current best known values for the constants K_{3}, K_{4}). Some related results of clear interest are also included (derived) in our discussion.
The improvements here obtained are relevant to numerical simulations, as the solutions are known to be smooth for t > t*. In particular, they are useful for numerical investigations of the Clay Millenium problem regarding the incompressible Navier-Stokes equations