Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions

Details Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions

2012-04-02

arxiv.org/abs/1204.0529v1

Mathematics

Analysis of PDEs

26 pages

Scientific paper

We show that the classical Cauchy problem for the incompressible 3d
Navier-Stokes equations with $(-1)$-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.

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