On Schrödinger and wave maps. (English) Zbl 1065.35105

Nahmod, Andrea R.

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) (ISBN 0-8218-2903-3/pbk). Contemp. Math. 320, 295-322 (2003).

This is a survey article presenting mainly the results of A. R. Nahmod, A. Stefanov and K. Uhlenbeck [Commun. Pure Appl. Math. 56, No. 1, 114–151 (2003; Zbl 1028.58018)] and 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.
For the entire collection see [Zbl 1013.00026].

Reviewer: Andreas Gastel (Düsseldorf)

MSC:

35J10	Schrödinger operator, Schrödinger equation
42B35	Function spaces arising in harmonic analysis
58J45	Hyperbolic equations on manifolds

Keywords:

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

Citations:

Zbl 1028.58018