We consider the energy critical Schrödinger map ∂tu=u∧δu 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 Q1 in the scale invariant norm Ḣ1 which generate finite time blow up solutions. We give in addition a sharp description of the corresponding singularity formation which occurs by concentration of a universal bubble of energy. where θ*∈R, u*∈Ḣ1, R is a rotation and the concentration rate is given for some κ(u)>0 by.
|Translated title of the contribution
|Blow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map
|Number of pages
|Comptes Rendus Mathematique
|Published - Mar 2011
All Science Journal Classification (ASJC) codes
- General Mathematics