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CATEGORIES:Partial Differential Equations seminar
SUMMARY:STRICHARTZ ESTIMATES FOR THE 2D AND 3D MASSLESS DI
RAC-COULOMB EQUATIONS - Elena Danesi
DTSTART;TZID=Europe/London:20240429T140000
DTEND;TZID=Europe/London:20240429T150000
UID:TALK215827AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/215827
DESCRIPTION:\nThe massless Dirac equation with a Coulomb poten
tial is interesting both from a physical and a mat
hematical point of view\; it appears in some physi
cal models\, for instance the 2D equation is used
to describe the dynamics of carbon atoms in a shee
t of non-perfect graphene\, and on the mathematica
l side the homogeneity of degree -1 of the potenti
al seems to have a critical behavior\, as |x| goes
to infinity\, since Strichartz estimates are know
n to hold for potentials that decay faster and the
re are examples of potentials decaying slower such
that the corresponding flows do not disperse.\nIn
this talk I will present a recent result concerni
ng Strichartz estimates for the solutions of the m
assless Dirac-Coulomb equation in 2 and 3 dimensio
n with additional angular regularity. It extends t
he result on R3 of Cacciafesta-Séré-Zhang and prov
ides completely new estimates on R2. As an applica
tion we will discuss a local well-posedness result
for a nonlinear system.
LOCATION:MR13
CONTACT:Dr Greg Taujanskas
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