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.
@article{JEDP_2012____A9_0, author = {Tataru, Daniel}, title = {Schr\"odinger maps}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {9}, pages = {1--11}, publisher = {Groupement de recherche 2434 du CNRS}, year = {2012}, doi = {10.5802/jedp.92}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jedp.92/} }
Tataru, Daniel. Schrödinger maps. Journées équations aux dérivées partielles (2012), article no. 9, 11 p. doi : 10.5802/jedp.92. http://www.numdam.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 ., preprint available on arxiv. | Zbl
[5] J. Krieger, W. Schlag Concentration compactness for critical wave maps, EMS Monographs in Mathematics, 2012 | MR
[6] F. Merle, P. Raphaël, I. Rodnianski, Blow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map, preprint. | MR
[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[9] T. Tao, Gauges for the Schrödinger map, http://www.math.ucla.edu/ tao/preprints/Expository (unpublished).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
Cited by Sources: