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The large time behavior of solutions to 3D Navier–Stokes equations with nonlinear damping

✍ Scribed by Zaihong Jiang; Mingxuan Zhu

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
111 KB
Volume
35
Category
Article
ISSN
0170-4214

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✦ Synopsis

This paper studies the Cauchy problem of the 3D Navier–Stokes equations with nonlinear damping term | u | ^β−1^u (β ≥ 1). For β ≥ 3, we derive a decay rate of the L^2^‐norm of the solutions. Then, the large time behavior is given by comparing the equation with the classic 3D Navier–Stokes equations. Copyright © 2011 John Wiley & Sons, Ltd.

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## Abstract In this paper we derive a decay rate of the __L__^2^‐norm of the solution to the 3‐D Navier–Stokes equations. Although the result which is proved by Fourier splitting method is well known, our method is new, concise and direct. Moreover, it turns out that the new method established here