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Mathematics > Analysis of PDEs

arXiv:1804.10588 (math)
[Submitted on 27 Apr 2018 (v1), last revised 16 Jul 2018 (this version, v2)]

Title:Green functions of conormal derivative problems for stationary Stokes system

Authors:Jongkeun Choi, Hongjie Dong, Doyoon Kim
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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.
Comments: minor revision; accepted in Journal of Mathematical Fluid Mechanics
Subjects: Analysis of PDEs (math.AP)
MSC classes: 35J08, 35J57, 76N10, 76D07
Cite as: arXiv:1804.10588 [math.AP]
  (or arXiv:1804.10588v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.10588
Related DOI: https://doi.org/10.1007/s00021-018-0387-0

Submission history

From: Jongkeun Choi [view email]
[v1] Fri, 27 Apr 2018 16:53:53 UTC (20 KB)
[v2] Mon, 16 Jul 2018 14:51:56 UTC (22 KB)
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