Maximum modulus estimate for the solution of the Stokes equations

Tong Keun Chang; Hi Jun Choe

doi:10.1016/j.jde.2013.01.009

Maximum modulus estimate for the solution of the Stokes equations

Tong Keun Chang, Hi Jun Choe

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

11 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 language	English
Pages (from-to)	2682-2704
Number of pages	23
Journal	Journal of Differential Equations
Volume	254
Issue number	7
DOIs	https://doi.org/10.1016/j.jde.2013.01.009
Publication status	Published - 2013 Apr 1

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Access to Document

10.1016/j.jde.2013.01.009

Cite this

@article{dd541afa64e3411fa6d1cf8817c9107a,

title = "Maximum modulus estimate for the solution of the Stokes equations",

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.",

author = "Chang, {Tong Keun} and Choe, {Hi Jun}",

year = "2013",

month = apr,

day = "1",

doi = "10.1016/j.jde.2013.01.009",

language = "English",

volume = "254",

pages = "2682--2704",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "7",

}

TY - JOUR

T1 - Maximum modulus estimate for the solution of the Stokes equations

AU - Chang, Tong Keun

AU - Choe, Hi Jun

PY - 2013/4/1

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.

UR - http://www.scopus.com/inward/record.url?scp=84873247662&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84873247662&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2013.01.009

DO - 10.1016/j.jde.2013.01.009

M3 - Article

AN - SCOPUS:84873247662

SN - 0022-0396

VL - 254

SP - 2682

EP - 2704

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 7

ER -

Maximum modulus estimate for the solution of the Stokes equations

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this