Lp-Theory of the Stokes equation in a half space

Wolfgang Desch*, Matthias Georg Hieber, Jan Prüss

*この研究の対応する著者

研究成果: Article査読

85 被引用数 (Scopus)

抄録

In this paper, we investigate Lp-estimates for the solution of the Stokes equation in a half space H where 1 <p <∞. It is shown that the solution of the Stokes equation is governed by an analytic semigroup on B U Cσ(H), C0,σ(H) or Lσ (H). From the operatortheoretical point of view it is a surprising fact that the corresponding result for Lσ 1(H) does not hold true. In fact, there exists an L1 -function f satisfying div f = 0 such that the solution of the corresponding resolvent equation with right hand side f does not belong to L1 . Taking into account however a recent result of Kozono on the nonlinear Navier-Stokes equation, the L1 -result is not surprising and even natural. We also show that the Stokes operator admits a R-bounded H-calculus on Lp for 1 <p <∞ and obtain as a consequence maximal Lp-Lq-regularity for the solution of the Stokes equation.

本文言語English
ページ(範囲)115-142
ページ数28
ジャーナルJournal of Evolution Equations
1
1
出版ステータスPublished - 2001
外部発表はい

ASJC Scopus subject areas

  • 生態、進化、行動および分類学

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