For weak solutions to the three-dimensional Navier-Stokes equations the interior regularity problem for the renormalized velocity $u(1+|u|^2)^{-\alpha/2}$ and pressure $p(1+|u|^2)^{-\beta/2}$ is investigated. If a velocity component is locally semibounded and $\nabla u$ slightly more regular than suitable weak solutions the regularity estimates for the renormalized velocity are improved. Furthermore, estimates for the negative part of a renormalized pressure are presented.
@article{1238418795,
author = {Frehse, Jens and Specovius-Neugebauer, Maria},
title = {Renormalized estimates for solutions to the Navier-Stokes equation},
journal = {Funct. Approx. Comment. Math.},
volume = {40},
number = {1},
year = {2009},
pages = { 11-32},
language = {en},
url = {http://dml.mathdoc.fr/item/1238418795}
}
Frehse, Jens; Specovius-Neugebauer, Maria. Renormalized estimates for solutions to the Navier-Stokes equation. Funct. Approx. Comment. Math., Tome 40 (2009) no. 1, pp. 11-32. http://gdmltest.u-ga.fr/item/1238418795/