A remark on the global regularity for the 3D Navier–Stokes equations

A remark on the global regularity for the 3D Navier–Stokes equations

In this paper, we investigate the case of Prodi–Serrin type regularity criterion involving u3 and ∂3uh. More precisely, it is shown that Leray’s weak solutions of the three-dimensional Navier–Stokes equations become regular if the third component of velocity (or the gradient of the velocity field) s...

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Veröffentlicht in:Applied mathematics letters 2016-07, Vol.57, p.126-131
1. Verfasser: Qian, Chenyin
Format: Artikel
Sprache:eng
Schlagworte:
3D Navier–Stokes equations
Criteria
Leray–Hopf weak solution
Mathematical analysis
Navier-Stokes equations
Regularity
Regularity criterion
Three dimensional
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Zusammenfassung:In this paper, we investigate the case of Prodi–Serrin type regularity criterion involving u3 and ∂3uh. More precisely, it is shown that Leray’s weak solutions of the three-dimensional Navier–Stokes equations become regular if the third component of velocity (or the gradient of the velocity field) satisfies the additional end-point Prodi–Serrin type condition.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2016.01.016