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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Mathematical Study of Certain Geophysical Models:
Global Regularity and Finite-time Blowup Results -
Titi\, E (UC\, Irvine and Weizmann Institute of S
cience)
DTSTART;TZID=Europe/London:20131203T091500
DTEND;TZID=Europe/London:20131203T101500
UID:TALK49145AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/49145
DESCRIPTION:The basic problem faced in geophysical \nuid dynam
ics 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 ana
lytically. In this talk I will discuss the main ob
stacles in proving the global regularity for the t
hree-dimensional Navier-Stokes equations and their
geophysical counterparts. However\, taking advant
age of certain geophysical balances and situations
\, such as geostrophic balance and the shallowness
of the ocean and atmosphere\, geophysicists deriv
e more simplied and manageable models which are e
asier to study analytically. In particular\, I wil
l present the global well-posedness for the three-
dimensional Benard convection problem in porous\n
media\, and the global regularity for a three-dime
nsional viscous planetary geostrophic models. Eve
n though the primitive equations look as if they a
re more dicult to study analytically than the thr
ee-dimensional Navier-Stokes equations I will show
\, on the one hand\, that the viscous primitive eq
uations have a unique global (in time) regular sol
ution for all initial data. On the other hand\, I
will show that in the non-viscous (inviscid) case
there is a one-parameter family of initial data fo
r which the corresponding smooth solutions develop
nite-time singularities (blowup).\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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