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 journalArticle

    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
    JournalMathematische Annalen
    DOIs
    Publication statusAccepted/In press - 2018 Jan 1

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    Stokes Operator
    Maximal Regularity
    Exterior Domain
    Moving Boundary
    Navier-Stokes Equations
    Navier-Stokes System
    Invertible
    Existence Theorem
    Dirichlet Boundary Conditions
    Generalise
    Interval
    Operator

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

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