On the Lp-Lq maximal regularity of the Neumann problem for the Stokes equations in a bounded domain

Yoshihiro Shibata*, Senjo Shimizu

*この研究の対応する著者

研究成果: Article査読

66 被引用数 (Scopus)

抄録

In this paper, we prove the Lp-Lq maximal regularity of solutions to the Neumann problem for the Stokes equations with non-homogeneous boundary condition and divergence condition in a bounded domain. The result was first stated by Solonnikov V. A. Solonnikov, On the transient motion of an isolated volume of viscous incompressible fluid, Math. USSR Izvest. 31 (1988), 381405., but he assumed that p = q > 3 and considered only the finite time interval case. In this paper, we consider not only the case: 1 < p, q < but also the infinite time interval case. Especially, we obtain the Lp-Lq maximal regularity theorem with exponential stability on the infinite time interval. Our method can be applied to any initial boundary value problem for the equation of parabolic type with suitable boundary condition which generates an analytic semigroup, for example the Stokes equation with non-slip, slip or Robin boundary conditions.

本文言語English
ページ(範囲)157-209
ページ数53
ジャーナルJournal fur die Reine und Angewandte Mathematik
615
DOI
出版ステータスPublished - 2008 2月 1

ASJC Scopus subject areas

  • 数学 (全般)
  • 応用数学

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