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arXiv · 1204.5444

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

Andrea R. Nahmod·Nataša Pavlović·Gigliola Staffilani
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Abstract

In this paper we show that after suitable data randomization there exists a large set of super-critical periodic initial data, in $H^{-α}({\mathbb T}^d)$ for some $α(d) > 0$, 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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Andrea R. Nahmod, Nataša Pavlović, Gigliola Staffilani. 2013-02-25. Almost sure existence of global weak solutions for super-critical Navier-Stokes equations. https://arxiv.org/abs/1204.5444

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