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UID:news469@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20181228T194637
DTSTART;TZID=Europe/Zurich:20140924T161500
SUMMARY:Seminar Analysis: Camilla Nobili (Max Planck Institute for Mathemat
 ics in the Sciences\, Leipzig)
DESCRIPTION:We consider Rayleigh-Bénard convection at finite Prandtl numbe
 r as modelled by the Boussinesq equation. We are interested in the scaling
  of the average upward heat transport\, the Nusselt number Nu\, in terms o
 f the Rayleigh number Ra\, and the Prandtl number Pr.\\r\\nPhysically  mot
 ivated  heuristics  suggest  the  scaling Nu∼Ra1⁄3 and Nu∼Ra1/2 depe
 nding on Pr\, in different regimes. \\r\\nIn this talk I present a rigorou
 s upper bound for Nu reproducing both physical scalings in some parameter 
 regimes up to logarithms.  This is obtained by a (logarithmically failing)
  maximal regularity estimate inL1and inL1for the nonstationary Stokes equa
 tion with forcing term given by the buoyancy term and the nonlinear term\,
  respectively.  This is a joint work with Felix Otto and Antoine Choffrut.
X-ALT-DESC:\nWe consider Rayleigh-Bénard convection at finite Prandtl numb
 er as modelled by the Boussinesq equation. We are interested in the scalin
 g of the average upward heat transport\, the Nusselt number Nu\, in terms 
 of the Rayleigh number Ra\, and the Prandtl number Pr.\nPhysically  motiva
 ted  heuristics  suggest  the  scaling Nu∼Ra<sup>1⁄3</sup> and Nu∼Ra
 <sup>1/2</sup> depending on Pr\, in different regimes. \nIn this talk I pr
 esent a rigorous upper bound for Nu reproducing both physical scalings in 
 some parameter regimes up to logarithms.  This is obtained by a (logarithm
 ically failing) maximal regularity estimate inL1and inL1for the nonstation
 ary Stokes equation with forcing term given by the buoyancy term and the n
 onlinear term\, respectively.  This is a joint work with Felix Otto and An
 toine Choffrut.
DTEND;TZID=Europe/Zurich:20140924T171500
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