Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions
arXiv:1204.0529
Abstract
We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with -homogeneous initial data has a global scale-invariant solution which is smooth for positive times. Our main technical tools are local-in-space regularity estimates near the initial time, which are of independent interest.
26 pages