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Blow up dynamics for smooth data equivariant solutions to the energy critical Schrodinger map problem | | Frank Merle
; Pierre Raphael
; Igor Rodnianski
; | | Date: |
21 Feb 2011 | | Abstract: | We consider the energy critical Schr"odinger map to the 2-sphere for
equivariant initial data of homotopy number k=1. We show the existence of a set
of smooth initial data arbitrarily close to the ground state harmonic map in
the scale invariant norm which generates finite time blow up solutions. We give
a sharp description of the corresponding singularity formation which occurs by
concentration of a universal bubble of energy. The concentration rate is given
by $$lambda(t)=kappa(u)frac{T-t}{|log (T-t)|^2}(1+o(1))$$ for some
$kappa(u)>0$. The detailed proofs of the results will appear in a companion
paper. | | Source: | arXiv, 1102.4308 | | Services: | Forum | Review | PDF | Favorites | |
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