Depletion of nonlinearity in the pressure force driving Navier-Stokes flows: nonlinear depletion in NS flows

Chuong Van Tran; Xinwei Yu

doi:10.1088/0951-7715/28/5/1295

Depletion of nonlinearity in the pressure force driving Navier-Stokes flows: nonlinear depletion in NS flows

Chuong Van Tran, Xinwei Yu

Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The dynamics of the velocity norms ||u||_Lq for q ≥ 3, in Navier-Stokes flows is studied. The pressure term that drives this dynamics has a high degree of nonlinear depletion, which owes its origin to a genuine negative correlation between |u| and |∇|u||, among other things. Under viscous effects, such depletion may give rise to
mild growth of ||u||_Lq. We explore the possibility of
non-singular growth of ||u||_Lq.

Original language	English
Pages (from-to)	1295-1306
Number of pages	12
Journal	Nonlinearity
Volume	28
DOIs	https://doi.org/10.1088/0951-7715/28/5/1295
Publication status	Published - 17 Apr 2015

Keywords

Navier-Stokes equations
Depletion of nonlinearity
Global regularity

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© 2015 IOP Publishing Ltd & London Mathematical Society. This work is made available online with express permission from the publisher. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.iopscience.iop.org. Depletion of nonlinearity in the pressure force driving Navier-Stokes flows: nonlinear depletion in NS flows Tran, C. V. & Yu, X. 17 Apr 2015 In : Nonlinearity. 28, p. 1295-1306
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T2 - nonlinear depletion in NS flows

AU - Tran, Chuong Van

AU - Yu, Xinwei

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N2 - The dynamics of the velocity norms ||u||Lq for q ≥ 3, in Navier-Stokes flows is studied. The pressure term that drives this dynamics has a high degree of nonlinear depletion, which owes its origin to a genuine negative correlation between |u| and |∇|u||, among other things. Under viscous effects, such depletion may give rise to mild growth of ||u||Lq. We explore the possibility of non-singular growth of ||u||Lq.

AB - The dynamics of the velocity norms ||u||Lq for q ≥ 3, in Navier-Stokes flows is studied. The pressure term that drives this dynamics has a high degree of nonlinear depletion, which owes its origin to a genuine negative correlation between |u| and |∇|u||, among other things. Under viscous effects, such depletion may give rise to mild growth of ||u||Lq. We explore the possibility of non-singular growth of ||u||Lq.

KW - Navier-Stokes equations

KW - Depletion of nonlinearity

KW - Global regularity

UR - https://www.scopus.com/pages/publications/84946182703

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DO - 10.1088/0951-7715/28/5/1295

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SP - 1295

EP - 1306

JO - Nonlinearity

JF - Nonlinearity

ER -

Depletion of nonlinearity in the pressure force driving Navier-Stokes flows: nonlinear depletion in NS flows

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Keywords

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