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Asymptotics for null-timelike boundary problems for general linear wave equations

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Abstract

We study the linear wave equation □gu = 0 in Bondi-Sachs coordinates, for an asymptotically flat Lorentz metric g. We consider the null-timelike boundary problem, where an initial value is given on the null surface τ = 0 and a boundary value on the timelike surface r = r0. We obtain spacetime Hp-estimates of ru for r > r0 and derive an asymptotic expansion of ru in terms of 1/r as r → ∞.

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Acknowledgements

The first author was supported by National Science Foundation of USA (Grant No. DMS-1404596). The second author was supported by National Natural Science Foundation of China (Grant No. 11571019). The authors thank Xiao Zhang for many helpful discussions.

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Authors and Affiliations

  1. Department of Mathematics, University of Notre Dame, Notre Dame, IN, 46556, USA

    Qing Han

  2. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Lin Zhang

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  1. Qing Han
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  2. Lin Zhang
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Correspondence to Lin Zhang.

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Han, Q., Zhang, L. Asymptotics for null-timelike boundary problems for general linear wave equations. Sci. China Math. 64, 111–128 (2021). https://doi.org/10.1007/s11425-018-9492-6

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  • DOI: https://doi.org/10.1007/s11425-018-9492-6

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