Global Well-posedness for 2D Nonlinear Wave Equations without Compact Support
Analysis of PDEs
2018-12-17 v1
Abstract
In the significant work of [2], Alinhac proved the global existence of small solutions for 2D quasilinear wave equations under the null conditions. The proof heavily relies on the fact that the initial data have compact support [22]. Whether this constraint can be removed or not is still unclear. In this paper, for fully nonlinear wave equations under the null conditions, we prove the global well-posedness for small initial data without compact support. Moreover, we apply our result to a class of quasilinear wave equations.
Keywords
Cite
@article{arxiv.1712.02130,
title = {Global Well-posedness for 2D Nonlinear Wave Equations without Compact Support},
author = {Yuan Cai and Zhen Lei and Nader Masmoudi},
journal= {arXiv preprint arXiv:1712.02130},
year = {2018}
}
Comments
To appear in J. Math. Pures Appl