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

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

2012-04-24

arxiv.org/abs/1204.5444v1

Mathematics

Analysis of PDEs

20 pages

Scientific paper

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.

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