Modified wave operators for a scalar quasilinear wave equation satisfying the weak null condition
Analysis of PDEs
2021-03-22 v3
Abstract
We prove the existence of the modified wave operators for a scalar quasilinear wave equation satisfying the weak null condition. This is accomplished in three steps. First, we derive a new reduced asymptotic system for the quasilinear wave equation by modifying H\"{o}rmander's method. Next, we construct an approximate solution, by solving our new reduced system given some scattering data at infinite time. Finally, we prove that the quasilinear wave equation has a global solution which agrees with the approximate solution at infinite time.
Keywords
Cite
@article{arxiv.2002.05355,
title = {Modified wave operators for a scalar quasilinear wave equation satisfying the weak null condition},
author = {Dongxiao Yu},
journal= {arXiv preprint arXiv:2002.05355},
year = {2021}
}
Comments
51 pages. v2: terminology changed, introduction revised, typos corrected. v3: funding information added, typos corrected