Almost sure existence of global weak solutions for super-critical Navier-Stokes equations

Andrea R. Nahmod; Nataša Pavlović; Gigliola Staffilani

Almost sure existence of global weak solutions for super-critical Navier-Stokes equations

Analysis of PDEs 2013-02-27 v3

Authors: Andrea R. Nahmod , Nataša Pavlović , Gigliola Staffilani

Abstract

In this paper we show that after suitable data randomization there exists a large set of super-critical periodic initial data, in $H^{-\alpha}({\mathbb T}^d)$ for some $\alpha(d) > 0$ , for both 2d and 3d Navier-Stokes equations for which global energy bounds are proved. As a consequence, we obtain almost sure super-critical global weak solutions. We also show that in 2d these global weak solutions are unique.

Keywords

navier-stokes equations global weak solutions super-critical data randomization almost sure existence energy bounds

Cite

@article{arxiv.1204.5444,
  title  = {Almost sure existence of global weak solutions for super-critical Navier-Stokes equations},
  author = {Andrea R. Nahmod and Nataša Pavlović and Gigliola Staffilani},
  journal= {arXiv preprint arXiv:1204.5444},
  year   = {2013}
}

Comments

22 pages, a revised argument in Section 5, the $d=3$ case

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