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Zbl 1065.35105
Nahmod, Andrea R.
On Schrödinger and wave maps. (English)
[A] Beckner, William (ed.) et al., Harmonic analysis at Mount Holyoke. Proceedings of an AMS-IMS-SIAM joint summer research conference, Mount Holyoke College, South Hadley, MA, USA, June 25--July 5, 2001. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 320, 295-322 (2003). ISBN 0-8218-2903-3/pbk

This is a survey article presenting mainly the results of {\it A. R. Nahmod, A. Stefanov} and {\it K. Uhlenbeck} [Commun. Pure Appl. Math. 56, No. 1, 114--151 (2003; Zbl 1028.58018)] and {\it A. R. Nahmod, A. Stefanov, K. Uhlenbeck} [Commun. Anal. Geom. 11, 49--83 (2003)]. The subject are Schrödinger maps and wave maps (which are two different hyperbolic versions of harmonic maps) from Minkowski space into compact Riemannian manifolds. The survey focusses on the results and stresses similarities in the methods used, including methods from harmonic analysis and gauge theory.
[Andreas Gastel (Düsseldorf)]

MSC 2000:: *35J10 Schroedinger operator
42B35 Function spaces arising in harmonic analysis
58J45 Hyperbolic equations

Keywords: nonlinear hyperbolic system; well-posedness; wave maps; Schrödinger maps; regularity; harmonic analysis; gauge theory

Citations: Zbl 1028.58018

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