Abstract
In this paper, we study the asymptotic behavior of solutions to the three-dimensional incompressible Navier-Stokes equations (NSE) with periodic boundary conditions and potential body forces. In particular, we prove that the Foias-Saut asymptotic expansion for the regular solutions of the NSE in fact holds in all Gevrey classes. This strengthens the previous result obtained in Sobolev spaces by Foias-Saut. By using the Gevrey-norm technique of Foias-Temam, the proof of our improved result simplifies the original argument of Foias-Saut, thereby, increasing its adaptability to other dissipative systems. Moreover, the expansion is extended to all Leray-Hopf weak solutions.
Original language | English |
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Pages (from-to) | 167-190 |
Number of pages | 24 |
Journal | Asymptotic Analysis |
Volume | 104 |
Issue number | 3-4 |
DOIs | |
State | Published - 2017 |
Keywords
- 3D Navier-Stokes equations
- Gevrey class
- Leray-Hopf weak solutions
- asymptotic expansions
- eventual regularity