Long-time asymptotic expansions for Navier-Stokes equations with power-decaying forces

Dat Cao, Luan Hoang

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


The Navier-Stokes equations for viscous, incompressible fluids are studied in the three-dimensional periodic domains, with the body force having an asymptotic expansion, when time goes to infinity, in terms of power-decaying functions in a Sobolev-Gevrey space. Any Leray-Hopf weak solution is proved to have an asymptotic expansion of the same type in the same space, which is uniquely determined by the force, and independent of the individual solutions. In case the expansion is convergent, we show that the next asymptotic approximation for the solution must be an exponential decay. Furthermore, the convergence of the expansion and the range of its coefficients, as the force varies are investigated.

Original languageEnglish
Pages (from-to)569-606
Number of pages38
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Issue number2
StatePublished - Apr 1 2020


  • Navier-Stokes
  • asymptotic expansion
  • power-decaying


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