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Communications in Mathematical Physics

, Volume 330, Issue 1, pp 69–105 | Cite as

Blow Up Dynamics for Equivariant Critical Schrödinger Maps

  • Galina PerelmanEmail author
Article

Abstract

For the Schrödinger map equation \({u_t = u \times \triangle u \, {\rm in} \, \mathbb{R}^{2+1}}\) , with values in S 2, we prove for any \({\nu > 1}\) the existence of equivariant finite time blow up solutions of the form \({u(x, t) = \phi(\lambda(t) x) + \zeta(x, t)}\) , where \({\phi}\) is a lowest energy steady state, \({\lambda(t) = t^{-1/2-\nu}}\) and \({\zeta(t)}\) is arbitrary small in \({\dot H^1 \cap \dot H^2}\) .

Keywords

Global Existence Remote Region Sulem Convergent Expansion Bootstrap Assumption 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.LAMA, UMR CNRS 8050Université Paris-Est CréteilCréteil CedexFrance

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