Kavli Affiliate: Yi Zhou
| First 5 Authors: Sheng Wang, Yi Zhou, , ,
| Summary:
Wei-Yue Ding cite{Ding 2002} proposeed a proposition about Schr"odinger map
flow in 2002 International Congress of Mathematicians in Beijing, which is
called Wei-Yue Ding conjecture by Rodnianski-Rubinstein-Staffilani
cite{Rodnianski 2009}. They proved cite{Rodnianski 2009} that Schr"odinger
map flow for maps from the real line into K"ahler manifolds and for maps from
the circle into Riemann surfaces is globally well-posed which is the first
significant advance in this conjecture by translating the Schr"odinger map
flow into nonlinear Schr"odinger-type equations or (systems) and partially
solved this conjecture. In this article, we will derive a new div-curl type
lemma and combined it with energy and “momentum" balance law to get some
space-time estimates. Based on this, we prove the Schr"odinger map flow for
maps from the circle into K"ahler manifolds is globally regular, this settles
the Wei-Yue Ding’s conjecture.
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