期刊
ASYMPTOTIC ANALYSIS
卷 104, 期 3-4, 页码 167-190出版社
IOS PRESS
DOI: 10.3233/ASY-171429
关键词
3D Navier-Stokes equations; Leray-Hopf weak solutions; asymptotic expansions; eventual regularity; Gevrey class
资金
- NSF [DMS-1412796]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1412796] Funding Source: National Science Foundation
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.
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