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

Hao Jia UNIVERSITY OF MINNESOTA Vladimir Sverak UNIVERSITY OF MINNESOTA

Analysis of PDEs mathscidoc:1804.03008

Distinguished Paper Award in 2018

Invent math, 196, (1), 233-265, 2014.4
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 tech- nical tools are local-in-space regularity estimates near the initial time, which are of independent interest.
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@inproceedings{hao2014local-in-space,
  title={Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions},
  author={Hao Jia, and Vladimir Sverak},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180427113547413079074},
  booktitle={Invent math},
  volume={196},
  number={1},
  pages={233-265},
  year={2014},
}
Hao Jia, and Vladimir Sverak. Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions. 2014. Vol. 196. In Invent math. pp.233-265. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180427113547413079074.
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