Global existence of null-form wave equations on small asymptotically Euclidean manifolds

Abstract

We prove the global existence of the small solutions to the Cauchy problem for quasilinear wave equations satisfying the null condition on $(R^3,g)$, where the metric $g$ is a small perturbation of the flat metric and approaches the Euclidean metric like $(1+|x|{)}^{-a}$ with $a>1$. Global and almost global existence for systems without the null condition are also discussed for certain small time-dependent perturbations of the flat metric in the appendix.

Final version, to appear in Journal of Functional Analysis

References in corpus (4)

• The Glassey conjecture with radially symmetric data
• On the quasilinear wave equations in time dependent inhomogeneous media
• Concerning the Strauss conjecture on asymptotically Euclidean manifolds
• Decay estimates of a tangential derivative to the light cone for the wave equation and their application

Cited by in corpus (11)

• On the quasilinear wave equations in time dependent inhomogeneous media
• Long time existence for semilinear wave equations on asymptotically flat space-times
• The Glassey conjecture on asymptotically flat manifolds
• A Vector Field Method for Radiating Black Hole Spacetimes
• Global nonlinear stability of large dispersive solutions to the Einstein equations
• Global solutions of nonlinear wave equations with large energy
• Global existence for semilinear damped wave equations in relation with the Strauss conjecture
• Uniform boundedness of highest norm for 2D quasilinear wave
• Uniform estimates for 2D quasilinear wave
• The Glassey conjecture for nontrapping obstacles
• The weak null condition on Kerr backgrounds