### Abstract

Equivariant wave maps from double-struck S sign^{2} × ℝ into double-struck S sign^{2} have smooth, stationary solutions which are critical points of the energy subject to constant charge. These solutions are globally stable under equivariant perturbations. Consequently, there exists a large set of initial data, with no degree or energy restrictions, for which the Cauchy problem is globally well-posed.

Original language | English (US) |
---|---|

Pages (from-to) | 231-256 |

Number of pages | 26 |

Journal | Communications in Mathematical Physics |

Volume | 185 |

Issue number | 1 |

State | Published - 1997 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Communications in Mathematical Physics*,

*185*(1), 231-256.

**On the stability of stationary wave maps.** / Shatah, Jalal; Tahvildar-Zadeh, A. Shadi.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 185, no. 1, pp. 231-256.

}

TY - JOUR

T1 - On the stability of stationary wave maps

AU - Shatah, Jalal

AU - Tahvildar-Zadeh, A. Shadi

PY - 1997

Y1 - 1997

N2 - Equivariant wave maps from double-struck S sign2 × ℝ into double-struck S sign2 have smooth, stationary solutions which are critical points of the energy subject to constant charge. These solutions are globally stable under equivariant perturbations. Consequently, there exists a large set of initial data, with no degree or energy restrictions, for which the Cauchy problem is globally well-posed.

AB - Equivariant wave maps from double-struck S sign2 × ℝ into double-struck S sign2 have smooth, stationary solutions which are critical points of the energy subject to constant charge. These solutions are globally stable under equivariant perturbations. Consequently, there exists a large set of initial data, with no degree or energy restrictions, for which the Cauchy problem is globally well-posed.

UR - http://www.scopus.com/inward/record.url?scp=0031115723&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031115723&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031115723

VL - 185

SP - 231

EP - 256

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -