Geometric renormalization of large energy wave maps

dc.creatorTao, Terence
dc.date2004-11-16
dc.date.accessioned2026-07-07T05:14:22Z
dc.date.available2026-07-07T05:14:22Z
dc.descriptionThere has been much progress in recent years in understanding the existence problem for wave maps with small critical Sobolev norm (in particular for two-dimensional wave maps with small energy); a key aspect in that theory has been a renormalization procedure (either a geometric Coulomb gauge, or a microlocal gauge) which converts the nonlinear term into one closer to that of a semilinear wave equation. However, both of these renormalization procedures encounter difficulty if the energy of the solution is large. In this report we present a different renormalization, based on the harmonic map heat flow, which works for large energy wave maps from two dimensions to hyperbolic spaces. We also observe an intriguing estimate of ``non-concentration'' type, which asserts roughly speaking that if the energy of a wave map concentrates at a point, then it becomes asymptotically self-similar.
dc.description28 pages, no figures, submitted, Forges les Eaux conference proceedings
dc.identifierhttps://arxiv.org/abs/math/0411354
dc.identifierhttp://arxiv.org/abs/math/0411354
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73253
dc.subjectAnalysis of PDEs
dc.subject35J10
dc.titleGeometric renormalization of large energy wave maps
dc.typetext

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