Renormalization and Blow up for Charge One Equivariant Critical Wave Maps
نویسنده
چکیده
We prove the existence of equivariant finite time blow-up solutions for the wave map problem from R2+1 → S2 of the form u(t, r) = Q(λ(t)r)+R(t, r) where u is the polar angle on the sphere, Q(r) = 2 arctan r is the ground state harmonic map, λ(t) = t−1−ν , and R(t, r) is a radiative error with local energy going to zero as t→ 0. The number ν > 1 2 can be described arbitrarily. This is accomplished by first ”renormalizing” the blow-up profile, followed by a perturbative analysis.
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تاریخ انتشار 2006