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arXiv · 1308.1588

Almost sure existence of Navier-Stokes Equations with randomized data in the whole space

Robin Ming Chen·Dehua Wang·Song Yao·Cheng Yu
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Abstract

This paper considers the supercritical Navier-Stokes equations posed in the whole space $\R^d$, with suitably randomized initial data, in the weak solution setting. The global weak solutions are constructed for a large set of initial data in $H^{-s}(\R^d)$ for some $s>0$ via a probabilistic argument, and this in turn implies the almost sure existence.

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Robin Ming Chen, Dehua Wang, Song Yao, Cheng Yu. 2013-10-27. Almost sure existence of Navier-Stokes Equations with randomized data in the whole space. https://arxiv.org/abs/1308.1588

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