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- W2964278468 abstract "We consider the energy critical Schrodinger 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 H˙1 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 energyu(t,x)−eΘ⁎RQ1(xλ(t))→u⁎in H˙1 as t→Twhere Θ⁎∈R, u⁎∈H˙1, R is a rotation and the concentration rate is given for some κ(u)>0 byλ(t)=κ(u)T−t|log(T−t)|2(1+o(1))as t→T." @default.
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- W2964278468 date "2011-03-01" @default.
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- W2964278468 title "Blow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map" @default.
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- W2964278468 doi "https://doi.org/10.1016/j.crma.2011.01.026" @default.
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