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

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.

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

Cited by in corpus (1)

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