The Probabilistic Method and large initial data for Generalized Navier-Stokes systems

Jean C. Cortissoz

The Probabilistic Method and large initial data for Generalized Navier-Stokes systems

Analysis of PDEs 2011-09-12 v2 Probability

Authors: Jean C. Cortissoz

Abstract

In this paper we introduce a probabilistic approach to show the existence of initial data with arbitrarily large $L^2(\mathbb{R}^3)$ , $\dot{H}^{1/2}(\mathbb{R}^3)$ and $\mathcal{PM}^2$ -norms for which a Generalized Navier-Stokes system generate a global regular solution. More precisely, we show that from a certain family of possible large initial data most of them give raise to global regular solutions to a given Generalized Navier-Stokes system.

Keywords

navier-stokes equations point processes

Cite

@article{arxiv.1105.3871,
  title  = {The Probabilistic Method and large initial data for Generalized Navier-Stokes systems},
  author = {Jean C. Cortissoz},
  journal= {arXiv preprint arXiv:1105.3871},
  year   = {2011}
}

Comments

21 pages. A better discussion on the probabilistic setting has been included. Conditions on the initial data, as the divergence free condition and real-valuedness, have been taken care of. A section on how the arguments can be generalized has been added

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