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

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)33-72
Number of pages40
JournalAsymptotic Analysis
Volume107
Issue number1-2
DOIs
Publication statusPublished - 2018 Jan 1

Keywords

  • Exterior domains
  • Free boundary problem
  • L-L decay estimate
  • Stokes equations
  • Without surface tension

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'On the L<sub>p</sub>-L<sub>q</sub> decay estimate for the Stokes equations with free boundary conditions in an exterior domain'. Together they form a unique fingerprint.

  • Cite this