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SUMMARY:1D Burgers Turbulence: a Model Case for the Kolmogorov Theory - Al
 exandre Boritchev (Ecole Polytechnique\, France)
DTSTART:20120530T150000Z
DTEND:20120530T163000Z
UID:TALK37758@talks.cam.ac.uk
CONTACT:Marc Briant
DESCRIPTION:The Kolmogorov 1941 theory (K41) is\, in a way\, the starting 
 point for\nall models of turbulence. In particular\, K41 and\ncorrections 
 to it provide estimates of small-scale quantities such as\nincrements and 
 energy spectrum for a 3D turbulent flow. However\,\nbecause of the well-kn
 own difficulties involved in studying 3D\nturbulent flow\, there are no ri
 gorous results confirming or infirming\nthose\npredictions.\n        Here\
 , we consider a well-known simplified model for 3D turbulence:\nBurgulence
 \, or turbulence for the 1D Burgers equation. In the\nspace-periodic case 
 with a stochastic white in time and smooth in\nspace force\, we give sharp
  estimates for small-scale quantities such\nas\nincrements and energy spec
 trum. Namely\, we confirm results of the\narticle of Aurell\, Frisch\, Lut
 sko and Vergassola published in 1991\,\nusing some of their ideas. We use 
 SDE techniques (infinite-dimensional\nItô calculus) as well as classical 
 PDE techniques (maximum\nprinciple).
LOCATION:MR14\, CMS
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