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Journal of Mathematical Fluid Mechanics

, Volume 3, Issue 3, pp 213–230 | Cite as

A Decay Property of the Fourier Transform and its Application to the Stokes Problem

  • Y. Shibata
  • S. Shimizu

Abstract.

We prove an optimal relationship between the regularity of a function and the asymptotic behavior of its Fourier transform. As an application of this result we show L p -estimates for the Stokes semigroup in \( \Bbb R^n \) and \( {\Bbb R}_+^n \) when \( 1\leqq p\leqq \infty \).

Keywords. Fourier transform, decay property, Stokes flow, L1-estimate, $ L_{\infty}$-estimate. 

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Copyright information

© Birkhäuser Verlag, Basel, 2001

Authors and Affiliations

  • Y. Shibata
    • 1
  • S. Shimizu
    • 2
  1. 1.Department of Mathematical Sciences, School of Science and Engineering, Waseda University, Ohkubo 3-4-1, Shinjyuku-ku, Tokyo 169-8555, Japan, e-mail: yshibata@mn.waseda.ac.jpJP
  2. 2.Faculty of Engineering, Shizuoka University, Hamamatsu 432-8561, Japan, e-mail: tssshim@eng.shizuoka.ac.jpJP

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