Renormalization and blow up for charge one equivariant critical wave maps

• 成果类型: Article
• 署名作者: Krieger, J.; Schlag, W.; Tataru, D.
• 署名单位: Harvard University; University of Chicago; University of California System; University of California Berkeley
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-007-0089-3
• 发表日期: 2008
• 页码: 543-615
• 关键词: nonlinear schrodinger-equation; HARMONIC MAPS; global regularity; minkowski space; small energy; SINGULARITIES; dimensions; MANIFOLDS

摘要

We prove the existence of equivariant finite time blow-up solutions for the wave map problem from R2+ 1 -> S-2 of the form u( t, r) = Q(lambda( 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, lambda(t) = t(-1-nu), and R(t, r) is a radiative error with local energy going to zero as t -> 0. The number nu > 1/2 can be prescribed arbitrarily. This is accomplished by first renormalizing the blow-up profile, followed by a perturbative analysis.