Partial regularity of solution to generalized Navier-Stokes problem

0430423 - MÚ 2015 RIV PL eng J - Journal Article
Mácha, Václav
Partial regularity of solution to generalized Navier-Stokes problem.
Central European Journal of Mathematics. Roč. 12, č. 10 (2014), s. 1460-1483. ISSN 1895-1074
R&D Projects: GA ČR(CZ) GAP201/11/1304; GA ČR GA201/09/0917
Institutional support: RVO:67985840
Keywords : Stokes problem * Navier-Stokes problem * partial regularity
Subject RIV: BA - General Mathematics
Impact factor: 0.578, year: 2014
http://link.springer.com/article/10.2478%2Fs11533-014-0427-9

In the presented work, we study the regularity of solutions to the generalized Navier-Stokes problem up to a C2 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 Hausdor measure of a singular set, i.e. a complement of a set where a solution is Holder continuous. We use so-called indirect approach to show partial regularity, for dimension 2 we get even an empty set of singular points.
Permanent Link: http://hdl.handle.net/11104/0235366