Global Smooth Solutions and Large Time Behavior of the One-Dimensional Navier–Stokes Equations
✍ Scribed by Tao Pang
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 138 KB
- Volume
- 235
- Category
- Article
- ISSN
- 0022-247X
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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
## Communicated by S. Chen The main purpose of this paper is concerned with blow-up smooth solutions to Navier-Stokes-Poisson (N-S-P) equations. First, we present a sufficient condition on the blow up of smooth solutions to the N-S-P system. Then we construct a family of analytical solutions that