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Previous Prairie Seminars
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Titles and abstracts of talks
Carlos Kenig
Quantitative unique
continuation theorems for dispersive equations
In these lectures I will first recall some quantitative
unique
continuation theorems for elliptic and parabolic equations. The
elliptic one is a key ingredient in the recent proof by Bourgain and
Kenig of Anderson
localization for the Bernoulli model in higher dimensions. The
parabolic one is joint work of Escauriaza, Kenig, Ponce and Vega
and solves a conjecture of Landis-Oleinik (1974). After this, inspired
by the well-known uncertainty principle, we formulate and prove
analogous results for dispersive equations, including the Scrodinger
and KdV equations. This is joint work of Escauriaza, Kenig, Ponce and
Vega.
James Colliander
On blowup
solutions of the nonlinear Schroedinger equation with low
regularity initial data
The initial value
problem for the focusing cubic nonlinear Schroedinger equation (NLS) on R^2 is
locally well-posed for initial data in L^2. The L^2 norm is invaraint under
the dilation symmetry of solutions, so this problem is called L^2-critical.
Finite time blowup solutions of
this problem are known to exist. Qualitative properties, such as mass concentration, of blowup solutions
evolving from initial data much more regular than L^2 have been established.
This talk will describe recent work
toward a more descriptive
theory of blowup solutions in the setting of L^2 initial data. Also, some comparisons with
the (much less understood) blowup of L^2 supercritical NLS will be made.
Alexandru Ionescu
Low regularity solutions of the
Benjamin-Ono and the KP-I equations
I will talk about some recent joint work with Carlos
Kenig on local and
global well-posedness in low regularity spaces of the Benjamin-Ono and
the KP-I initial value problems.
Abstracts of contributed talks
Organizers:
Estela A. Gavosto, KU
Marianne Korten, KSU
Charles Moore, KSU
Rodolfo H. Torres, KU
Contact Information:
marianne@math.ksu.edu
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