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

Hao Jia; Vladimír Šverák

doi:10.1007/s00222-013-0468-x

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

Hao Jia, Vladimír Šverák

Mathematics

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97 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	233-265
Number of pages	33
Journal	Inventiones Mathematicae
Volume	196
Issue number	1
DOIs	https://doi.org/10.1007/s00222-013-0468-x
State	Published - Apr 2014

Bibliographical note

Funding Information:
This work was supported in part by grant DMS 1101428 from the National Science Foundation.

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

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