Asymptotic completeness for a scalar quasilinear wave equation satisfying the weak null condition

Abstract

In this paper, we prove the first asymptotic completeness result for a scalar quasilinear wave equation satisfying the weak null condition. The main tool we use in the study of this equation is the geometric reduced system introduced in arXiv:2002.05355. Starting from a global solution $u$ to the quasilinear wave equation, we rigorously show that well chosen asymptotic variables solve the same reduced system with small error terms. This allows us to recover the scattering data for our system, as well as to construct a matching exact solution to the reduced system.

114 pages. This paper continues the work in arXiv:2002.05355. v2: introduction revised, typos corrected

References in corpus (2)

• Modified wave operators for a scalar quasilinear wave equation satisfying the weak null condition
• Nonlinear wave equations

Cited by in corpus (1)

• Timelike asymptotics for global solutions to a scalar quasilinear wave equation satisfying the weak null condition