Some regularity criteria of a weak solution to the 3D Navier–Stokes equations in a domain

Some regularity criteria of a weak solution to the 3D Navier–Stokes equations in a domain

We give some regularity criterion (of a weak - L p Serrin type) of a weak solution to the 3D Navier–Stokes equations in a bounded domain Ω ⊂ R 3 with a smooth boundary. In particular, in case of the half space, we give a regularity condition of a weak solution with respect to a tangential component...

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Veröffentlicht in:Archiv der Mathematik 2021-08, Vol.117 (2), p.215-225
1. Verfasser: Kim, Jae-Myoung
Format: Artikel
Sprache:eng
Schlagworte:
Domains
Fluid dynamics
Fluid flow
Mathematical analysis
Mathematics
Mathematics and Statistics
Navier-Stokes equations
Physical Sciences
Regularity
Science & Technology
Smooth boundaries
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Zusammenfassung:We give some regularity criterion (of a weak - L p Serrin type) of a weak solution to the 3D Navier–Stokes equations in a bounded domain Ω ⊂ R 3 with a smooth boundary. In particular, in case of the half space, we give a regularity condition of a weak solution with respect to a tangential component of the velocity flow vector.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-021-01613-0