Constrained Wave Equations and Wave Maps

Jalal Shatah, Chongchun Zeng

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)383-404
Number of pages22
JournalCommunications in Mathematical Physics
Volume239
Issue number3
DOIs
StatePublished - Aug 2003

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wave equations
Wave equation
Penalization Method
Implicit Function Theorem
Multiscale Analysis
Formal Analysis
Well-posedness
theorems
Oscillation
Converge
oscillations
Motion
Term
Interaction
interactions

ASJC Scopus subject areas

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

Cite this

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

In: Communications in Mathematical Physics, Vol. 239, No. 3, 08.2003, p. 383-404.

Research output: Contribution to journalArticle

Shatah, Jalal ; Zeng, Chongchun. / Constrained Wave Equations and Wave Maps. In: Communications in Mathematical Physics. 2003 ; Vol. 239, No. 3. pp. 383-404.
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