Unconditional well-posedness for wave maps

Nader Masmoudi, Fabrice Planchon

Research output: Contribution to journalArticle

Abstract

We prove a uniqueness theorem for solutions to the wave map equation in the natural class, namely (u, ∂ tu) ∈ C([0, T); H d/2) × C 1([0, T); H d/2-1) in dimension d ≥ 4. This is achieved by estimating the difference of two solutions at a lower regularity level. In order to reduce to the Coulomb gauge, one has to localize the gauge change in suitable cones, as well as to estimate the difference between the frames and connections associated with each solution and to take advantage of the assumption that the target manifold has bounded curvature.

Original languageEnglish (US)
Pages (from-to)223-237
Number of pages15
JournalJournal of Hyperbolic Differential Equations
Volume9
Issue number2
DOIs
StatePublished - Jun 2012

Fingerprint

Well-posedness
Gauge
Uniqueness Theorem
Cone
Regularity
Curvature
Target
Estimate
Class

Keywords

  • uniqueness
  • Wave map

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis

Cite this

Unconditional well-posedness for wave maps. / Masmoudi, Nader; Planchon, Fabrice.

In: Journal of Hyperbolic Differential Equations, Vol. 9, No. 2, 06.2012, p. 223-237.

Research output: Contribution to journalArticle

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