A sufficiency class for global (in time) solutions to the 3D Navier–Stokes equations
✍ Scribed by T.L. Gill; W.W. Zachary
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 310 KB
- Volume
- 73
- Category
- Article
- ISSN
- 0362-546X
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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
## 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