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SUMMARY:Analysis of Oceanic and Tropical Atmospheric with Moisture Models:
  Global Regularity\, Finite-time Blowup and Singular Limit Behavior - Edri
 ss S. Titi (University of Cambridge)
DTSTART:20190502T130000Z
DTEND:20190502T134500Z
UID:TALK123901@talks.cam.ac.uk
CONTACT:Ferdia Sherry
DESCRIPTION:In this talk I will present some recent results concerning glo
 bal regularity of certain geophysical models. This will include the three-
 dimensional primitive equations with various anisotropic viscosity and tur
 bulence mixing diffusion\, and certain tropical atmospheric models with mo
 isture. Moreover\, in the non-viscous (inviscid) case it can be shown that
  there is a one-parameter family of initial data for which the correspondi
 ng smooth solutions of the primitive equations develop finite-time\nsingul
 arities (blowup).\n\nCapitalizing on the above results\, we can provide ri
 gorous justification of the derivation of the Primitive Equations of plane
 tary scale oceanic dynamics from the three-dimensional Navier-Stokes equat
 ions\, for vanishing small values of the aspect ratio of the depth to hori
 zontal width. Specifically\, we can show that the Navier-Stokes equations\
 , after being scaled appropriately by the small aspect ratio parameter of 
 the physical domain\, converge strongly to the primitive equations\, globa
 lly and uniformly in time\, and that the convergence rate is of the same o
 rder as the aspect ratio parameter. Furthermore\, I will also consider the
  singular limit behavior of a tropical atmospheric model with moisture\, a
 s ε → 0\, where ε > 0 is a moisture phase transition small convective 
 adjustment relaxation time parameter.\n
LOCATION:Centre for Mathematical Sciences\, MR2
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