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Multisolitons for the Defocusing Energy Critical Wave Equation with Potentials

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Abstract

We construct multi-soliton solutions to the defocusing energy critical wave equation with potentials in \({\mathbb{R}^{3}}\) and study their asymptotic stability in the energy space based on both regular and reversed Strichartz estimates developed in [GC3]. We also study related scattering problems in the stable case. Since each soliton decays slowly with rate \({\frac{1}{\left\langle x\right\rangle }}\) , some refined estimates for the charge transfer model are also established.

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Authors and Affiliations

  1. Department of Mathematics, The University of Chicago, 5734 South University Avenue, Chicago, IL, 60637, USA

    Gong Chen

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  1. Gong Chen
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Correspondence to Gong Chen.

Additional information

Communicated by W. Schlag

This work is part of the author’s Ph.D. thesis at the University of Chicago.

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Chen, G. Multisolitons for the Defocusing Energy Critical Wave Equation with Potentials. Commun. Math. Phys. 364, 45–82 (2018). https://doi.org/10.1007/s00220-018-3170-4

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  • DOI: https://doi.org/10.1007/s00220-018-3170-4

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