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.
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The authors would like to thank the referees for careful reading and helpful comments.
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Communicated by R. Shvydkoy
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).
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Choi, J., Dong, H. & Kim, D. Green Functions of Conormal Derivative Problems for Stationary Stokes System. J. Math. Fluid Mech. 20, 1745–1769 (2018). https://doi.org/10.1007/s00021-018-0387-0
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DOI: https://doi.org/10.1007/s00021-018-0387-0