TY  - GEN 
T1  - A generalization of some regularity criteria to the Navier-Stokes equations involving one velocity component
A1  - Axmann, Šimon
A1  - Pokorný, Milan
ED  - Galdi, Giovanni P.
ED  - Heywood, John G.
ED  - Rannacher, Rolf
TI  - Recent Developments of Mathematical Fluid Mechanics
T3  - Advances in Mathematical Fluid Mechanics
Y1  - 2014
PB  - Birkhauser-Verlag
KW  - global regularity
KW  - Incompressible Navier–Stokes equations
KW  - regularity criteria.
N2  - We present generalizations of results concerning conditional global regularity of weak Leray–Hopf solutions to incompressible Navier– Stokes equations presented by Zhou and Pokorny´ in articles [15], [17], and [18]; see also [13]. We are able to replace the condition on one velocity compo- nent (or its gradient) by a corresponding condition imposed on a projection of the velocity (or its gradient) onto a more general vector field. Comparing to our other recent results from [1], the conditions imposed on the projection are more restrictive here, however due to the technique used in [1], there appeared a specific additional restriction on geometrical properties of the reference field, which could be omitted here.
M1  - Preprint project = NCMM
M1  - Preprint year = 2014
M1  - Preprint number = 11
M1  - Preprint ID = NCMM/2014/11
ER  -