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SUMMARY:STRICHARTZ ESTIMATES FOR THE 2D AND 3D MASSLESS DIRAC-COULOMB EQUA
 TIONS - Elena Danesi
DTSTART:20240429T130000Z
DTEND:20240429T140000Z
UID:TALK215827@talks.cam.ac.uk
CONTACT:Dr Greg Taujanskas
DESCRIPTION:\nThe massless Dirac equation with a Coulomb potential is inte
 resting both from a physical and a mathematical point of view\; it appears
  in some physical models\, for instance the 2D equation is used to describ
 e the dynamics of carbon atoms in a sheet of non-perfect graphene\, and on
  the mathematical side the homogeneity of degree -1 of the potential seems
  to have a critical behavior\, as |x| goes to infinity\, since Strichartz 
 estimates are known to hold for potentials that decay faster and there are
  examples of potentials decaying slower such that the corresponding flows 
 do not disperse.\nIn this talk I will present a recent result concerning S
 trichartz estimates for the solutions of the massless Dirac-Coulomb equati
 on in 2 and 3 dimension with additional angular regularity. It extends the
  result on R3 of Cacciafesta-Séré-Zhang and provides completely new esti
 mates on R2. As an application we will discuss a local well-posedness resu
 lt for a nonlinear system.
LOCATION:MR13
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