A conformal-type energy inequality on hyperboloids and its application to quasi-linear wave equation in $\mathbb{R}^{3+1}$

Yue Ma; Hongjing Huang

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arXiv · 1711.00498

A conformal-type energy inequality on hyperboloids and its application to quasi-linear wave equation in $\mathbb{R}^{3+1}$

Yue Ma·Hongjing Huang

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Abstract

In the present work, we will develop a conformal inequality in the hyperbolic foliation context which is analogous to the conformal inequality in the classical time-constant foliation context. Then as an application, we will apply this a priori estimate to the problem of global existence of quasi-linear wave equations in three spatial dimensions under null condition. With the aid of this inequality, we can establish more precise decay estimates on the global solution.

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Yue Ma, Hongjing Huang. 2017-11-01. A conformal-type energy inequality on hyperboloids and its application to quasi-linear wave equation in $\mathbb{R}^{3+1}$. https://arxiv.org/abs/1711.00498

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