### Abstract

In this paper we establish that wave maps can be obtained by a penalization method if the initial data is well prepared. When the data is not well prepared, we prove that the solution of the penalized equation converges weakly to the solution of the system of coupled equations obtained in [11] by a multi-scale formal analysis. In particular, the interaction between the rapid normal oscillations and the tangential motions creates a new term in the limit system whose well-posedness is proved by using the Nash-Moser Implicit Function Theorem.

Original language | English (US) |
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Pages (from-to) | 383-404 |

Number of pages | 22 |

Journal | Communications In Mathematical Physics |

Volume | 239 |

Issue number | 3 |

DOIs | |

State | Published - Aug 1 2003 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Shatah, J., & Zeng, C. (2003). Constrained Wave Equations and Wave Maps.

*Communications In Mathematical Physics*,*239*(3), 383-404. https://doi.org/10.1007/s00220-003-0887-4