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Communications in Mathematical Physics

, Volume 298, Issue 1, pp 139–230 | Cite as

Energy Dispersed Large Data Wave Maps in 2 + 1 Dimensions

  • Jacob Sterbenz
  • Daniel TataruEmail author
Open Access
Article

Abstract

In this article we consider large data Wave-Maps from \({\mathbb R^{2+1}}\) into a compact Riemannian manifold \({(\mathcal{M},g)}\), and we prove that regularity and dispersive bounds persist as long as a certain type of bulk (non-dispersive) concentration is absent. This is a companion to our concurrent article [21], which together with the present work establishes a full regularity theory for large data Wave-Maps.

Keywords

High Modulation Strichartz Estimate Global Regularity Canonical Extension Bilinear Estimate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowlegements

The authors would like to thank Manos Grillakis, Sergiu Klainerman, Joachim Krieger, Matei Machedon, Igor Rodnianski, and Wilhelm Schlag for many stimulating discussions over the years regarding the wave-map problem. We would also especially like to thank Terry Tao for several key discussions on the nature of induction-on-energy type proofs.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2010

Open AccessThis is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaSan DiegoUSA
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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