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

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.

arXiv comment49 pages

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• Remarks on basic calculus in hyperboloidal foliation