Maximal regularity of the Stokes operator in an exterior domain with moving boundary and application to the Navier–Stokes equations

Reinhard Farwig, Hideo Kozono, David Wegmann

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Consider the (Navier–) Stokes system on an exterior domain with moving boundary and Dirichlet boundary conditions. In 2003 Saal proved that the Stokes operator in a domain with moving boundary has the property of maximal regularity provided that the operator is invertible. Hence his result can be applied if the domain is bounded or by adding a shift to the Stokes operator if the domain is unbounded or the time interval is finite. In this paper, we will generalize his result to a result global in time if the reference domain is an exterior domain. Finally, we will apply this result to the Navier–Stokes equations to obtain a global in time existence theorem for small data.

Original languageEnglish
Pages (from-to)949-972
Number of pages24
JournalMathematische Annalen
Volume375
Issue number3-4
DOIs
Publication statusPublished - 2019 Dec 1

ASJC Scopus subject areas

  • Mathematics(all)

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