On the Lp-Lq decay estimate for the Stokes equations with free boundary conditions in an exterior domain

Yoshihiro Shibata*

*この研究の対応する著者

研究成果: Article査読

5 被引用数 (Scopus)

抄録

This paper deals with the Lp-Lq decay estimate of the C0 analytic semigroup {T (t)}t≥0 associated with the perturbed Stokes equations with free boundary conditions in an exterior domain. The problem arises in the study of free boundary problem for the Navier-Stokes equations in an exterior domain. We proved that ||δjT(t)f||Lp ≤ Cp,qt - j/2 - N/2(1/q - 1/p) ||f||Lq (j = 0,1) provided that 1 < q ≤ p ≤ ∞ and q ≠ ∞. Compared with the non-slip boundary condition case, the gradient estimate is better, which is important for the application to proving global well-posedness of free boundary problem for the Navier-Stokes equations. In our proof, it is crucial to prove the uniform estimate of the resolvent operator, the resolvent parameter ranging near zero.

本文言語English
ページ(範囲)33-72
ページ数40
ジャーナルAsymptotic Analysis
107
1-2
DOI
出版ステータスPublished - 2018

ASJC Scopus subject areas

  • 数学 (全般)

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