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Global Regularity of Wave Maps from R2+1 to H2. Small Energy

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Abstract

We demonstrate that Wave Maps with smooth initial data and small energy from R2+1 to the Lobatchevsky plane stay smooth globally in time. Our method is similar to the one employed in [18]. However, the multilinear estimates required are considerably more involved and present novel technical challenges. In particular, we shall have to work with a modification of the functional analytic framework used in [30], [33], [18].

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Authors and Affiliations

  1. Department of Mathematics, Fine Hall, Princeton University, Princeton, NJ, 08544, USA

    Joachim Krieger

  2. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    Joachim Krieger

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  1. Joachim Krieger
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Communicated by P. Constantin

Acknowledgement. The author would like to thank his Ph. D. advisor Sergiu Klainerman for important advice and encouragement, as well as Kenji Nakanishi, Igor Rodnianski, Terence Tao and Daniel Tataru for helpful discussions. He is also indebted to the referee for pointing out errors and suggesting improvements for the manuscript.

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Krieger, J. Global Regularity of Wave Maps from R2+1 to H2. Small Energy. Commun. Math. Phys. 250, 507–580 (2004). https://doi.org/10.1007/s00220-004-1088-5

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  • DOI: https://doi.org/10.1007/s00220-004-1088-5

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