Fundamental solutions for stationary Stokes systems with measurable coefficients

Jongkeun Choi; Minsuk Yang

doi:10.1016/j.jde.2017.05.005

Fundamental solutions for stationary Stokes systems with measurable coefficients

Jongkeun Choi, Minsuk Yang

Department of Mathematics

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

11 Citations (Scopus)

Abstract

We establish the existence and the pointwise bound of the fundamental solution for the stationary Stokes system with measurable coefficients in the whole space R^d, d≥3, under the assumption that weak solutions of the system are locally Hölder continuous. We also discuss the existence and the pointwise bound of the Green function for the Stokes system with measurable coefficients on Ω, where Ω is an unbounded domain such that the divergence equation is solvable. Such a domain includes, for example, half space and an exterior domain.

Original language	English
Pages (from-to)	3854-3893
Number of pages	40
Journal	Journal of Differential Equations
Volume	263
Issue number	7
DOIs	https://doi.org/10.1016/j.jde.2017.05.005
Publication status	Published - 2017 Oct 5

Bibliographical note

Funding Information:
The authors would like to express their sincerely gratitude to the referee for careful reading and for many helpful comments and suggestions. We also thank Tongkeun Chang for valuable comments. J. Choi was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2014R1A1A2054865 ). M. Yang has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government ( MSIP ) (No. 2016R1C1B2015731 ).

Publisher Copyright:
© 2017 Elsevier Inc.

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.jde.2017.05.005

Cite this

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title = "Fundamental solutions for stationary Stokes systems with measurable coefficients",

abstract = "We establish the existence and the pointwise bound of the fundamental solution for the stationary Stokes system with measurable coefficients in the whole space Rd, d≥3, under the assumption that weak solutions of the system are locally H{\"o}lder continuous. We also discuss the existence and the pointwise bound of the Green function for the Stokes system with measurable coefficients on Ω, where Ω is an unbounded domain such that the divergence equation is solvable. Such a domain includes, for example, half space and an exterior domain.",

author = "Jongkeun Choi and Minsuk Yang",

note = "Funding Information: The authors would like to express their sincerely gratitude to the referee for careful reading and for many helpful comments and suggestions. We also thank Tongkeun Chang for valuable comments. J. Choi was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2014R1A1A2054865 ). M. Yang has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government ( MSIP ) (No. 2016R1C1B2015731 ). Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

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AU - Yang, Minsuk

N1 - Funding Information: The authors would like to express their sincerely gratitude to the referee for careful reading and for many helpful comments and suggestions. We also thank Tongkeun Chang for valuable comments. J. Choi was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2014R1A1A2054865 ). M. Yang has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government ( MSIP ) (No. 2016R1C1B2015731 ). Publisher Copyright: © 2017 Elsevier Inc.

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N2 - We establish the existence and the pointwise bound of the fundamental solution for the stationary Stokes system with measurable coefficients in the whole space Rd, d≥3, under the assumption that weak solutions of the system are locally Hölder continuous. We also discuss the existence and the pointwise bound of the Green function for the Stokes system with measurable coefficients on Ω, where Ω is an unbounded domain such that the divergence equation is solvable. Such a domain includes, for example, half space and an exterior domain.

AB - We establish the existence and the pointwise bound of the fundamental solution for the stationary Stokes system with measurable coefficients in the whole space Rd, d≥3, under the assumption that weak solutions of the system are locally Hölder continuous. We also discuss the existence and the pointwise bound of the Green function for the Stokes system with measurable coefficients on Ω, where Ω is an unbounded domain such that the divergence equation is solvable. Such a domain includes, for example, half space and an exterior domain.

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JO - Journal of Differential Equations

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Fundamental solutions for stationary Stokes systems with measurable coefficients

Abstract

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