On classical global solutions of nonlinear wave equations with large data

Shuang Miao; Long Pei; Pin Yu

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arXiv · 1407.4492

On classical global solutions of nonlinear wave equations with large data

Shuang Miao·Long Pei·Pin Yu

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Abstract

This paper studies the Cauchy problem for systems of semi-linear wave equations on $\mathbb{R}^{3+1}$ with nonlinear terms satisfying the null conditions. We construct future global-in-time classical solutions with arbitrarily large initial energy. The choice of the large Cauchy initial data is inspired by Christodoulou's characteristic initial data in his work \cite{Ch-08} on formation of black-holes. The main innovation of the current work is that we discovered a relaxed energy ansatz which allows us to prove decay-in-time-estimate. Therefore, the new estimates can also be applied in studying the Cauchy problem for Einstein equations.

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Shuang Miao, Long Pei, Pin Yu. 2014-07-16. On classical global solutions of nonlinear wave equations with large data. https://arxiv.org/abs/1407.4492

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