Global conservative weak solutions and global strong solutions for a class of weakly dissipative nonlinear dispersive wave equations
Analysis of PDEs
2026-03-24 v1
Abstract
In this paper, we study the global existence of solutions of the Cauchy problem for a class of weakly dissipative nonlinear dispersive wave equations . This includes the weakly dissipative Camassa-Holm equation and the weakly dissipative hyperelastic rod wave equation as special cases. Specifically, we establish three global existence results: one concerning the energy conservative weak solutions in a time-weighted space, and the other two concerning strong solutions, which include the cases of small initial data and sign-changing initial data. Our results recover and extend many known results for several classical models.
Keywords
Cite
@article{arxiv.2603.20649,
title = {Global conservative weak solutions and global strong solutions for a class of weakly dissipative nonlinear dispersive wave equations},
author = {Yiyao Lian and Zhenyu Wan and Zhaoyang Yin},
journal= {arXiv preprint arXiv:2603.20649},
year = {2026}
}