We obtain local estimates of the steady-state Stokes system "without pressure" near boundary. As an application of the local estimates, we prove the partial regularity up to the boundary for the stationary Navier-Stokes equations in a smooth domain in five dimension.
Bibliographical noteFunding Information:
Acknowledgement. This research was supported in part by NSF Grant No. DMS-9877055. The author expresses his deep gratitude to his advisor, Professor Vladimír Sˇverák for guidance and encouragement. The author also thanks referees for helpful comments.
All Science Journal Classification (ASJC) codes
- Mathematical Physics
- Condensed Matter Physics
- Computational Mathematics
- Applied Mathematics