Rooted trees for 3d Navier-Stokes equation

M. Gubinelli

First issued 10 November 2005 · PDF

Abstract

We establish a representation of a class of solutions of 3d Navier-Stokes equations in ${\mathbb R}^3$ using sums over rooted trees. We study the convergence properties of this series recovering in a simplified manner some results obtained recently by Sinai and other known results for solutions in spaces of pseudo-measures introduced initially by Le Jan and Sznitman. The series representation make sense also in the critical case where there exists global solutions for small initial data and it allows the study of their long-time or small-distance behavior.

Versions

1. Version 2 (arXiv v2) current
   6 March 2006
   arXiv comments: 11 pages
   PDF · LaTeX source · files and digests · arXiv:math-ph/0511041
2. Version 1 (arXiv v1)
   10 November 2005
   arXiv comments: 9 pages
   PDF · LaTeX source · files and digests · arXiv:math-ph/0511041

Cite

M. Gubinelli. Rooted trees for 3d Navier-Stokes equation. Papers of Massimiliano Gubinelli, 2005, version 2. https://mgubi.org/papers/paper/rooted-trees-navier-stokes/

Licence: arXiv.org non-exclusive license to distribute, assumed for submissions of 1991-2003; all other rights reserved to the authors

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