Maximum modulus estimate for the solution of the Stokes equations

Tong Keun Chang, Hi Jun Choe

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

A maximum modulus estimate for the nonstationary Stokes equations in C2 domain is found. The singular part and regular part of Poisson kernel are analyzed. The singular part consists of the gradient of single layer potential and the gradient of composite potential defined on only normal component of the boundary data. Furthermore, the normal velocity near the boundary is bounded if the boundary data is bounded. If the normal component of the boundary data is Dini-continuous and the tangential component of the boundary data is bounded, then the maximum modulus of velocity is bounded in whole domain.

Original languageEnglish
Pages (from-to)2682-2704
Number of pages23
JournalJournal of Differential Equations
Volume254
Issue number7
DOIs
Publication statusPublished - 2013 Apr 1

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Stokes Equations
Modulus
Estimate
Gradient
Composite materials
Single Layer Potential
Poisson Kernel
Composite

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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abstract = "A maximum modulus estimate for the nonstationary Stokes equations in C2 domain is found. The singular part and regular part of Poisson kernel are analyzed. The singular part consists of the gradient of single layer potential and the gradient of composite potential defined on only normal component of the boundary data. Furthermore, the normal velocity near the boundary is bounded if the boundary data is bounded. If the normal component of the boundary data is Dini-continuous and the tangential component of the boundary data is bounded, then the maximum modulus of velocity is bounded in whole domain.",
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Maximum modulus estimate for the solution of the Stokes equations. / Chang, Tong Keun; Choe, Hi Jun.

In: Journal of Differential Equations, Vol. 254, No. 7, 01.04.2013, p. 2682-2704.

Research output: Contribution to journalArticle

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AU - Chang, Tong Keun

AU - Choe, Hi Jun

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Y1 - 2013/4/1

N2 - A maximum modulus estimate for the nonstationary Stokes equations in C2 domain is found. The singular part and regular part of Poisson kernel are analyzed. The singular part consists of the gradient of single layer potential and the gradient of composite potential defined on only normal component of the boundary data. Furthermore, the normal velocity near the boundary is bounded if the boundary data is bounded. If the normal component of the boundary data is Dini-continuous and the tangential component of the boundary data is bounded, then the maximum modulus of velocity is bounded in whole domain.

AB - A maximum modulus estimate for the nonstationary Stokes equations in C2 domain is found. The singular part and regular part of Poisson kernel are analyzed. The singular part consists of the gradient of single layer potential and the gradient of composite potential defined on only normal component of the boundary data. Furthermore, the normal velocity near the boundary is bounded if the boundary data is bounded. If the normal component of the boundary data is Dini-continuous and the tangential component of the boundary data is bounded, then the maximum modulus of velocity is bounded in whole domain.

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