Regularity of a weak solution to the Navier--Stokes equations via one component of a spectral projection of vorticity

0428441 - MÚ 2015 RIV US eng J - Journal Article
Neustupa, Jiří - Penel, P.
Regularity of a weak solution to the Navier--Stokes equations via one component of a spectral projection of vorticity.
SIAM Journal on Mathematical Analysis. Roč. 46, č. 2 (2014), s. 1681-1700. ISSN 0036-1410. E-ISSN 1095-7154
R&D Projects: GA ČR GA13-00522S
Institutional support: RVO:67985840
Keywords : Navier-Stokes equations * weak solution * regularity criteria
Subject RIV: BA - General Mathematics
Impact factor: 1.265, year: 2014
http://epubs.siam.org/doi/abs/10.1137/120874874

We deal with a suitable weak solution v to the Navier--Stokes initial value problem in R3 x (0,T). We denote by omega+ a spectral projection of omega = curl v, defined by means of the spectral resolution of identity associated with the self-adjoint operator curl. We show that certain conditions imposed on omega+ or, alternatively, only omega+3(the third component of omega+)imply regularity of solution v.
Permanent Link: http://hdl.handle.net/11104/0233796