Mathematics Seminars - Friday 18 February; Friday 25 February 2011

[Mabilo]

M A T H E M A T I C S S E M I N A R S 2011

Friday, 18 February, at 14.30 hrs.

Paul André Razafimandimby
(University of Pretoria, South Africa)

"Some mathematical problems in the dynamics of stochastic second-grade 
fluids"

Abstract:
We investigate the stochastic equation for the motion of a second grade 
fluid filling a bounded (or periodic) domain of R2. Global existence of 
probabilistic weak solutions (and weak in the sense of partial 
differential equations) is expounded. We are also able to prove the 
pathwise uniqueness of solution. The two results yield the unique 
existence of probabilistic strong solution. On this basis we show that 
under suitable conditions on the data we can construct a sequence of 
solutions of the stochastic second grade fluid that converges to the 
probabilistic weak solution of the stochastic Navier-Stokes equations 
when the physical parameter α tends to zero. This is a joint work with 
Prof Mamadou Sango (Department of Mathematics and Applied Mathematics, 
University of Pretoria).

VENUE: Luigi Stasi Seminar Room, (ICTP Leonardo Building, first level)

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Friday, 25 February, at 14.30 hrs.

Dr. Andrés Pedroza
(University of Colima, Mexico)

"On the Bounded Isometry Conjecture"

Abstract:
F. Lalonde and L. Polterovich study the isometries of the group of 
Hamiltonian diffeomorphisms with respect to the Hofer metric. They 
defined a symplectic diffeomorphism ψ to be bounded, if the Hofer norm 
of [ψ, h] remains bounded as h varies on Ham(M, ω). The set of bounded 
symplectic diffeomorphisms, BI0 (M), of (M, ω) is a group that contains 
all Hamiltonian diffeomorphisms.
They conjectured that these two groups are equal, Ham(M, ω) = BI0 (M, ω) 
for every closed symplectic manifold. They prove this conjecture in the 
case when the symplectic manifold is a product of closed surfaces of 
positive genus. In this talk we give an outline of a new class of 
manifolds for which bounded isometry conjecture holds.

VENUE: Luigi Stasi Seminar Room, (ICTP Leonardo Building, first floor)