Decay properties of the Stokes semigroup in exterior domains with Neumann boundary condition

Yoshihiro Shibata, Senjo Shimizu

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    In this paper, we obtain local energy decay estimates and L p-Lq estimates of the solutions to the Stokes equations with Neumann boundary condition which is obtained as a linearized equation of the free boundary problem for the Navier-Stokes equations. Comparing with the non-slip boundary condition case, we have a better decay estimate for the gradient of the semigroup because of the null force at the boundary.

    Original languageEnglish
    Pages (from-to)1-34
    Number of pages34
    JournalJournal of the Mathematical Society of Japan
    Issue number1
    Publication statusPublished - 2007 Jan



    • L-L estimates
    • Local energy decay
    • Neumann boundary condition
    • Stokes semigroup

    ASJC Scopus subject areas

    • Mathematics(all)

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