### 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) |
---|---|

Pages (from-to) | 383-404 |

Number of pages | 22 |

Journal | Communications in Mathematical Physics |

Volume | 239 |

Issue number | 3 |

DOIs | |

State | Published - Aug 2003 |

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### ASJC Scopus subject areas

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

### Cite this

*Communications in Mathematical Physics*,

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

**Constrained Wave Equations and Wave Maps.** / Shatah, Jalal; Zeng, Chongchun.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 239, no. 3, pp. 383-404. https://doi.org/10.1007/s00220-003-0887-4

}

TY - JOUR

T1 - Constrained Wave Equations and Wave Maps

AU - Shatah, Jalal

AU - Zeng, Chongchun

PY - 2003/8

Y1 - 2003/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0042417239&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042417239&partnerID=8YFLogxK

U2 - 10.1007/s00220-003-0887-4

DO - 10.1007/s00220-003-0887-4

M3 - Article

VL - 239

SP - 383

EP - 404

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -