Asymptotic expansion in Gevrey spaces for solutions of Navier-Stokes equations

Luan T. Hoang, Vincent R. Martinez

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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 languageEnglish
Pages (from-to)167-190
Number of pages24
JournalAsymptotic Analysis
Issue number3-4
StatePublished - 2017


  • 3D Navier-Stokes equations
  • Gevrey class
  • Leray-Hopf weak solutions
  • asymptotic expansions
  • eventual regularity


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