Local-in-space Estimates near Initial Time for Weak Solutions of the Navier-stokes Equations and Forward Self-similar Solutions
نویسنده
چکیده
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.
منابع مشابه
Regularity of Forward-in-time Self-similar Solutions to the 3d Navier-stokes Equations
Any forward-in-time self-similar (localized-in-space) suitable weak solution to the 3D Navier-Stokes equations is shown to be infinitely smooth in both space and time variables. As an application, a proof of infinite space and time regularity of a class of a priori singular small self-similar solutions in the critical weak Lebesgue space L3,∞ is given.
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