On the stability of stationary wave maps

Jalal Shatah; A. Shadi Tahvildar-Zadeh

doi:10.1007/s002200050089

On the stability of stationary wave maps

Jalal Shatah, A. Shadi Tahvildar-Zadeh

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Pages (from-to)	231-256
Number of pages	26
Journal	Communications In Mathematical Physics
Volume	185
Issue number	1
DOIs	https://doi.org/10.1007/s002200050089
State	Published - 1997

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s002200050089

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abstract = "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.",

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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.

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On the stability of stationary wave maps

Abstract

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