Schrödinger maps

Daniel Tataru[1]

  • [1] University of California, Berkeley

Journées Équations aux dérivées partielles (2012)

  • page 1-11
  • ISSN: 0752-0360

Abstract

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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.

How to cite

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Tataru, Daniel. "Schrödinger maps." Journées Équations aux dérivées partielles (2012): 1-11. <http://eudml.org/doc/275417>.

@article{Tataru2012,
abstract = {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.},
affiliation = {University of California, Berkeley},
author = {Tataru, Daniel},
journal = {Journées Équations aux dérivées partielles},
language = {eng},
pages = {1-11},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Schrödinger maps},
url = {http://eudml.org/doc/275417},
year = {2012},
}

TY - JOUR
AU - Tataru, Daniel
TI - Schrödinger maps
JO - Journées Équations aux dérivées partielles
PY - 2012
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 11
AB - 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.
LA - eng
UR - http://eudml.org/doc/275417
ER -

References

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  1. I. Bejenaru, A. Ionescu, C. Kenig, D. Tataru, Global Schrödinger maps, Annals of Math., to appear Zbl1233.35112
  2. I. Bejenaru, A. Ionescu, C. Kenig, D. Tataru, Equivariant Schrödinger Maps in two spatial dimensions, preprint Zbl1326.35087MR3090782
  3. I. Bejenaru, D. Tataru, Near soliton evolution for equivariant Schrödinger Maps in two spatial dimensions, AMS Memoirs, to appear Zbl1303.58009
  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. Zbl1205.35294
  5. J. Krieger, W. Schlag Concentration compactness for critical wave maps, EMS Monographs in Mathematics, 2012 Zbl06004782MR2895939
  6. F. Merle, P. Raphaël, I. Rodnianski, Blow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map, preprint. Zbl1213.35139MR2783320
  7. Sterbenz, Jacob, Tataru, Daniel . Regularity of wave-maps in dimension 2+1. Comm. Math. Phys. 298 (2010), no. 1, 231–264. Zbl1218.35057MR2657818
  8. Sterbenz, Jacob, Tataru, Daniel . Energy dispersed large data wave maps in 2+1 dimensions. Comm. Math. Phys. 298 (2010), no. 1, 139–230. Zbl1218.35129MR2657817
  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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