Schrödinger maps
Daniel Tataru1
1 University of California, Berkeley
Journées équations aux dérivées partielles (2012), article no. 9, 11 p.

The Schrödinger map equation is a geometric Schrödinger model, closely associated to the harmonic heat flow and to the wave map equation. The aim of these notes is to describe recent and ongoing work on this model, as well as a number of related open problems.

DOI : 10.5802/jedp.92
Daniel Tataru 1

1 University of California, Berkeley 
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Daniel Tataru. Schrödinger maps. Journées équations aux dérivées partielles (2012), article  no. 9, 11 p. doi : 10.5802/jedp.92. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.92/

[1] I. Bejenaru, A. Ionescu, C. Kenig, D. Tataru, Global Schrödinger maps, Annals of Math., to appear

[2] I. Bejenaru, A. Ionescu, C. Kenig, D. Tataru, Equivariant Schrödinger Maps in two spatial dimensions, preprint | MR

[3] I. Bejenaru, D. Tataru, Near soliton evolution for equivariant Schrödinger Maps in two spatial dimensions, AMS Memoirs, to appear

[4] S. Gustafson, K. Nakanishi, T. Tsai, Asymptotic stability, concentration, and oscillation in harmonic map heat-flow, Landau-Lifshitz, and Schroedinger maps on ℝ 2 ., preprint available on arxiv. | Zbl

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[7] Sterbenz, Jacob, Tataru, Daniel . Regularity of wave-maps in dimension 2+1. Comm. Math. Phys. 298 (2010), no. 1, 231–264. | MR | Zbl

[8] Sterbenz, Jacob, Tataru, Daniel . Energy dispersed large data wave maps in 2+1 dimensions. Comm. Math. Phys. 298 (2010), no. 1, 139–230. | MR | Zbl

[9] T. Tao, Gauges for the Schrödinger map, http://www.math.ucla.edu/ tao/preprints/Expository (unpublished).

[10] T. Tao. Global regularity of wave maps VII. Control of delocalised or dispersed solutions arXiv:0908.0776

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