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SUMMARY:Mathematical Study of Certain Geophysical Models: Global Regularit
 y and Finite-time Blowup Results - Titi\, E (UC\, Irvine and Weizmann Inst
 itute of Science)
DTSTART:20131203T091500Z
DTEND:20131203T101500Z
UID:TALK49145@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The basic problem faced in geophysical \nuid dynamics is that 
 a mathematical description based only on fundamental physical principles\,
  the so-called the Primitive Equations"\, is often prohibitively expensive
  computationally\, and hard to study analytically. In this talk I will dis
 cuss the main obstacles in proving the global regularity for the three-dim
 ensional Navier-Stokes equations and their geophysical counterparts. Howev
 er\, taking advantage of certain geophysical balances and situations\, suc
 h as geostrophic balance and the shallowness of the ocean and atmosphere\,
  geophysicists derive more simplied and manageable models which are easie
 r to study analytically. In particular\, I will present the global well-po
 sedness for the three-dimensional Benard convection problem in porous\nme
 dia\, and the global regularity for a three-dimensional viscous planetary 
 geostrophic models.  Even though the primitive equations look as if they a
 re more dicult to study analytically than the three-dimensional Navier-St
 okes equations I will show\, on the one hand\, that the viscous primitive 
 equations have a unique global (in time) regular solution for all initial 
 data. On the other hand\, I will show that in the non-viscous (inviscid) c
 ase there is a one-parameter family of initial data for which the correspo
 nding smooth solutions develop nite-time singularities (blowup).\n
LOCATION:Seminar Room 1\, Newton Institute
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