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The almost global and global existence for quasi-linear wave equations with multiple-propagation speeds in high dimensions

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Abstract

In this paper, we consider the Cauchy problem for systems of quasi-linear wave equations with multiple propagation speeds in spatial dimensions n ≥ 4. The problem when the nonlinearities depend on both the unknown function and their derivatives is studied. Based on some Klainerman-Sideris type weighted estimates and space-time L 2 estimates, the results that the almost global existence for space dimensions n = 4 and global existence for n ≥ 5 of small amplitude solutions are presented.

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Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, P. R. China

    Yi Du

  2. School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, 510275, P. R. China

    Zheng An Yao

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  1. Yi Du
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  2. Zheng An Yao
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Correspondence to Yi Du.

Additional information

The first author is supported by National Natural Science Foundation of China (Grant No. 10826069) and China Postdoctoral Foundation (Grant No. 20090450902); the second author is supported by National Natural Science Foundation of China (Grant Nos. 10471156 and 10531040)

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Du, Y., Yao, Z.A. The almost global and global existence for quasi-linear wave equations with multiple-propagation speeds in high dimensions. Acta. Math. Sin.-English Ser. 27, 1205–1220 (2011). https://doi.org/10.1007/s10114-011-8017-2

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  • DOI: https://doi.org/10.1007/s10114-011-8017-2

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