In the presented work, we study the regularity of solutions to the generalized Navier-Stokes problem up to a C 2 boundary in dimensions two and three. The point of our generalization is an assumption that a deviatoric part of a stress tensor depends on a shear rate and on a pressure. We focus on estimates of the Hausdorff measure of a singular set which is defined as a complement of a set where a solution is Hölder continuous. We use so-called indirect approach to show partial regularity, for dimension 2 we get even an empty set of singular points.
@article{bwmeta1.element.doi-10_2478_s11533-014-0427-9,
author = {V\'aclav M\'acha},
title = {Partial regularity of solution to generalized Navier-Stokes problem},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {1460-1483},
zbl = {1303.35058},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-014-0427-9}
}
Václav Mácha. Partial regularity of solution to generalized Navier-Stokes problem. Open Mathematics, Tome 12 (2014) pp. 1460-1483. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-014-0427-9/
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