Asymptotic behavior of strong solutions to the 3D Navier–Stokes equations with a nonlinear damping term

Asymptotic behavior of strong solutions to the 3D Navier–Stokes equations with a nonlinear damping term

This paper deals with the asymptotic behavior of strong solutions to the 3D Navier–Stokes equations with a nonlinear damping term |u|β−1u(β≥3). First, we establish an upper bound for the difference between the solution of our equation and the heat equation in L2 space. Then, we optimize the upper bo...

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Veröffentlicht in:Nonlinear analysis 2012-09, Vol.75 (13), p.5002-5009
1. Verfasser: Jiang, Zaihong
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic properties
Damping
Fluid flow
Fourier analysis
Lower bound
Mathematical analysis
Navier–Stokes equations
Nonlinearity
Three dimensional
Upper bounds
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Zusammenfassung:This paper deals with the asymptotic behavior of strong solutions to the 3D Navier–Stokes equations with a nonlinear damping term |u|β−1u(β≥3). First, we establish an upper bound for the difference between the solution of our equation and the heat equation in L2 space. Then, we optimize the upper bound of decay for the solutions and obtain their algebraic lower bound by using Fourier Splitting method.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2012.04.014