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SUMMARY:Rigidity of long-term dynamics for the self-dual Chern-Simons-Schr
 ödinger equation within equivariance - Kihyun Kim (IHES)
DTSTART:20231106T140000Z
DTEND:20231106T150000Z
UID:TALK207751@talks.cam.ac.uk
CONTACT:Zexing Li
DESCRIPTION:We consider the long time dynamics for the self-dual Chern-Sim
 ons-Schrödinger equation (CSS) within equivariant symmetry. Being a gauge
 d 2D cubic nonlinear Schrödinger equation (NLS)\, (CSS) is L2-critical an
 d has pseudoconformal invariance and solitons. However\, there are two dis
 tinguished features of (CSS)\, the self-duality and non-locality\, which m
 ake the long time dynamics of (CSS) surprisingly rigid. For instance\, (i)
  any finite energy spatially decaying solutions to (CSS) decompose into at
  most one (!) modulated soliton and a radiation. Moreover\, (ii) in the hi
 gh equivariance case (i.e.\, the equivariance index ≥ 1)\, any smooth fi
 nite-time blow-up solutions even have a universal blow-up speed\, namely\,
  the pseudoconformal one. We explore this rigid dynamics using modulation 
 analysis\, combined with the self-duality and non-locality of the problem.
LOCATION:MR13
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