Regularity criteria for weak solutions to the Navier-Stokes equations in terms of spectral projections of vorticity and velocity

0562011 - MÚ 2023 RIV CH eng J - Journal Article
Neustupa, Jiří - Penel, P. - Yang, M.
Regularity criteria for weak solutions to the Navier-Stokes equations in terms of spectral projections of vorticity and velocity.
Journal of Mathematical Fluid Mechanics. Roč. 24, č. 4 (2022), č. článku 104. ISSN 1422-6928. E-ISSN 1422-6952
R&D Projects: GA ČR(CZ) GA22-01591S
Institutional support: RVO:67985840
Keywords : Navier-Stokes equations * weak solution * regularity criteria * vorticity
OECD category: Pure mathematics
Impact factor: 1.3, year: 2022
Method of publishing: Limited access
https://doi.org/10.1007/s00021-022-00728-w

We deal with a weak solution v to the Navier-Stokes initial value problem in R-3 x (0, T), that satisfies the strong energy inequality. We impose conditions on certain spectral projections of omega:= curly or just v, and we prove the regularity of solution v. The spectral projection is defined by means of the spectral resolution of identity associated with the self-adjoint operator curl.
Permanent Link: https://hdl.handle.net/11104/0334441