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Energy partition for the linear radial wave equation

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Abstract

We consider the radial free wave equation in all dimensions and derive asymptotic formulas for the space partition of the energy, as time goes to infinity. We show that the exterior energy estimate, which Duyckaerts et al. obtained in odd dimensions (Duyckaerts et al., J Eur Math Soc 13:533–599, 2011; J Eur Math Soc, 2013) fails in even dimensions. Positive results for restricted classes of data are obtained.

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Authors and Affiliations

  1. Centre de Mathématiques Laurent Schwartz, École polytechnique, CNRS, Route de Palaiseau, 91128 , Palaiseau Cedex, France

    Raphaël Côte

  2. Department of Mathematics, The University of Chicago, 5734 South University Avenue, Chicago, IL, 60615, USA

    Carlos E. Kenig & Wilhelm Schlag

Authors
  1. Raphaël Côte
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  2. Carlos E. Kenig
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  3. Wilhelm Schlag
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Corresponding author

Correspondence to Raphaël Côte.

Additional information

Support of the National Science Foundation DMS-0968472 for C. E. Kenig, and DMS-0617854, DMS-1160817 for W. Schlag is gratefully acknowledged. R. Côte wishes to thank the University of Chicago for its hospitality during the academic year 2011–2012. The authors thank Andrew Lawrie for comments on a preliminary version of this paper and the anonymous referee for suggestions which improved the presentation.

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Côte, R., Kenig, C.E. & Schlag, W. Energy partition for the linear radial wave equation. Math. Ann. 358, 573–607 (2014). https://doi.org/10.1007/s00208-013-0970-x

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  • DOI: https://doi.org/10.1007/s00208-013-0970-x

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