Local energy decay of solutions to the oseen equation in the exterior domains

Yuko Enomoto, Yoshihiro Shibata

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)


In this paper, we prove a local energy decay of the Oseen semigroup in the n-dimensional exterior domain (n ≥ 3). In the three dimensional exterior domain case, Kobayashi and Shibata [16] already proved the local energy decay. Our theorem is not only an extension of the results due to Kobayashi and Shibata to the n-dimensional case but also the complete study of the local energy decay theorem for the Oseen equation with optimal time decay rates. The local energy decay gives us a crucial step to obtain the Lp-L q estimates of the Oseen semigroup, which enable us to prove the unique existence of globally in time solutions to the Navier-Stokes equation in an exterior domain with small initial data in the Ln framework, and their properties of time decay.

Original languageEnglish
Pages (from-to)1291-1330
Number of pages40
JournalIndiana University Mathematics Journal
Issue number5
Publication statusPublished - 2004
Externally publishedYes


  • Exterior domain
  • Local energy decay
  • Oseen equation

ASJC Scopus subject areas

  • General Mathematics


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