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

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 o...

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Bibliographic Details
Published in:Inventiones mathematicae 2014-04, Vol.196 (1), p.233-265
Main Authors: Jia, Hao, Šverák, Vladimír
Format: Article
Language:English
Subjects:
Cauchy problem
Estimates
Mathematical analysis
Mathematics
Mathematics and Statistics
Navier-Stokes equations
Regularity
Self-similarity
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Summary: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.
ISSN:0020-9910
1432-1297
DOI:10.1007/s00222-013-0468-x