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SUMMARY:Tai-Peng Tsai (University of British Columbia)
DTSTART:20201214T153000Z
DTEND:20201214T170000Z
DTSTAMP:20260405T174811Z
UID:NSCM/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NSCM/10/">Th
 e Green tensor of the nonstationary Stokes system in the half space</a>\nb
 y Tai-Peng Tsai (University of British Columbia) as part of Nečas Seminar
  on Continuum Mechanics\n\n\nAbstract\nWe prove the first-ever pointwise e
 stimates of the (unrestricted) Green tensor and\nthe associated pressure t
 ensor of the nonstationary Stokes system in the half-space\, for\nevery sp
 ace dimension greater than one. The force field is not necessarily assumed
  to\nbe solenoidal. The key is to find a suitable Green tensor formula tha
 t maximizes the\ntangential decay\, showing in particular the integrabilit
 y of Green tensor derivatives.\nWith its pointwise estimates\, we show the
  symmetry of the Green tensor\, which in\nturn improves pointwise estimate
 s. We also study how the solutions converge to the\ninitial data\, and the
  (infinitely many) restricted Green tensors acting on solenoidal\nvector f
 ields. As applications\, we give new proofs of the existence of mild solut
 ions of the\nNavier-Stokes equations in Lq\, pointwise decay\, and uniform
 ly local Lq spaces in the\nhalf-space.\nThis talk is based on arXiv:2011.0
 0134\, a joint work with Kyungkeun Kang\, Baishun\nLai and Chen-Chih Lai.\
 n\nThis seminar session will exceptionally start at 16:30.\n
LOCATION:https://researchseminars.org/talk/NSCM/10/
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