Green Functions of Conormal Derivative Problems for Stationary Stokes System

Jongkeun Choi; Hongjie Dong; Doyoon Kim

doi:10.1007/s00021-018-0387-0

Green Functions of Conormal Derivative Problems for Stationary Stokes System

Jongkeun Choi, Hongjie Dong, Doyoon Kim

Department of Mathematics

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

10 Citations (Scopus)

Abstract

We study Green functions for stationary Stokes systems satisfying the conormal derivative boundary condition. We establish existence, uniqueness, and various estimates for the Green function under the assumption that weak solutions of the Stokes system are continuous in the interior of the domain. Also, we establish the global pointwise bound for the Green function under the additional assumption that weak solutions of the conormal derivative problem for the Stokes system are locally bounded up to the boundary. We provide some examples satisfying such continuity and boundedness properties.

Original language	English
Pages (from-to)	1745-1769
Number of pages	25
Journal	Journal of Mathematical Fluid Mechanics
Volume	20
Issue number	4
DOIs	https://doi.org/10.1007/s00021-018-0387-0
Publication status	Published - 2018 Dec 1

Keywords

Conormal derivative problem
Green function
Measurable coefficients
Stokes system

ASJC Scopus subject areas

Mathematical Physics
Condensed Matter Physics
Computational Mathematics
Applied Mathematics

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10.1007/s00021-018-0387-0

Cite this

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title = "Green Functions of Conormal Derivative Problems for Stationary Stokes System",

abstract = "We study Green functions for stationary Stokes systems satisfying the conormal derivative boundary condition. We establish existence, uniqueness, and various estimates for the Green function under the assumption that weak solutions of the Stokes system are continuous in the interior of the domain. Also, we establish the global pointwise bound for the Green function under the additional assumption that weak solutions of the conormal derivative problem for the Stokes system are locally bounded up to the boundary. We provide some examples satisfying such continuity and boundedness properties.",

keywords = "Conormal derivative problem, Green function, Measurable coefficients, Stokes system",

author = "Jongkeun Choi and Hongjie Dong and Doyoon Kim",

note = "Funding Information: The authors would like to thank the referees for careful reading and helpful comments. Jongkeun Choi was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1A6A3A03005168). Hongjie Dong was partially supported by the NSF under agreement DMS-1600593. Doyoon Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2016R1D1A1B03934369). Publisher Copyright: {\textcopyright} 2018, Springer Nature Switzerland AG.",

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doi = "10.1007/s00021-018-0387-0",

language = "English",

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T1 - Green Functions of Conormal Derivative Problems for Stationary Stokes System

AU - Choi, Jongkeun

AU - Dong, Hongjie

AU - Kim, Doyoon

N1 - Funding Information: The authors would like to thank the referees for careful reading and helpful comments. Jongkeun Choi was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1A6A3A03005168). Hongjie Dong was partially supported by the NSF under agreement DMS-1600593. Doyoon Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2016R1D1A1B03934369). Publisher Copyright: © 2018, Springer Nature Switzerland AG.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - We study Green functions for stationary Stokes systems satisfying the conormal derivative boundary condition. We establish existence, uniqueness, and various estimates for the Green function under the assumption that weak solutions of the Stokes system are continuous in the interior of the domain. Also, we establish the global pointwise bound for the Green function under the additional assumption that weak solutions of the conormal derivative problem for the Stokes system are locally bounded up to the boundary. We provide some examples satisfying such continuity and boundedness properties.

AB - We study Green functions for stationary Stokes systems satisfying the conormal derivative boundary condition. We establish existence, uniqueness, and various estimates for the Green function under the assumption that weak solutions of the Stokes system are continuous in the interior of the domain. Also, we establish the global pointwise bound for the Green function under the additional assumption that weak solutions of the conormal derivative problem for the Stokes system are locally bounded up to the boundary. We provide some examples satisfying such continuity and boundedness properties.

KW - Conormal derivative problem

KW - Green function

KW - Measurable coefficients

KW - Stokes system

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DO - 10.1007/s00021-018-0387-0

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SN - 1422-6928

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JO - Journal of Mathematical Fluid Mechanics

JF - Journal of Mathematical Fluid Mechanics

IS - 4

ER -

Green Functions of Conormal Derivative Problems for Stationary Stokes System

Abstract

Keywords

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