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

Robin Ming Chen; Dehua Wang; Song Yao; Cheng Yu

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

Analysis of PDEs 2013-10-29 v4

Authors: Robin Ming Chen , Dehua Wang , Song Yao , Cheng Yu

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.

Keywords

Navier-Stokes equations randomized data almost sure existence weak solutions supercritical regime probabilistic argument whole space

Cite

@article{arxiv.1308.1588,
  title  = {Almost sure existence of Navier-Stokes Equations with randomized data in the whole space},
  author = {Robin Ming Chen and Dehua Wang and Song Yao and Cheng Yu},
  journal= {arXiv preprint arXiv:1308.1588},
  year   = {2013}
}

Comments

This is a short version of our research note which draws heavily from arXiv:1204.5444

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