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SUMMARY:Xuefeng Liu (Niigata University\, Japan)
DTSTART:20200721T140000Z
DTEND:20200721T150000Z
DTSTAMP:20260423T024619Z
UID:CRM-CAMP/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CRM-CAMP/8/"
 >Solution verification for the stationary Navier-Stokes equation over boun
 ded non-convex 3D domains</a>\nby Xuefeng Liu (Niigata University\, Japan)
  as part of CRM CAMP (Computer-Assisted Mathematical Proofs) in Nonlinear 
 Analysis\n\n\nAbstract\nWe consider the solution verification for the stat
 ionary Navier-Stokes equation over a bounded non-convex 3D domain Ω. In 1
 999\, M.T. Nakao\, et al.\, reported a solution existence verification exa
 mple for the 2D square domain.  However\, it has been a difficult problem 
 to deal with general 2D domains and 3D domains\, due to the bottleneck pro
 blem in the  a priori error estimation for the linearized NS equation. Rec
 ently\, by extending the hypercircle method (Prage-Synge's theorem) to dea
 l with the divergence-free condition in the Stokes equation\, the explicit
  error estimation is constructed successfully based on a conforming finite
  element approach [arXiv:2006.02952]. Further\,  we succeeded in the solut
 ion existence verification for the stationary NS equation in several nonco
 nvex 3D domains.  In this talk\, I will show the latest progress on this t
 opic\, including the rigorous estimation of the eigenvalue of Stokes opera
 tor in 3D domains.\n
LOCATION:https://researchseminars.org/talk/CRM-CAMP/8/
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