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.
Bibliographical noteFunding 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 ).
© 2017 Elsevier Inc.
All Science Journal Classification (ASJC) codes
- Applied Mathematics