On the Cauchy problem for the Hunter-Saxton equation on the line
Analysis of PDEs
2021-01-01 v1
Abstract
In this paper, we consider the Cauchy problem for the Hunter-Saxton (HS) equation on the line. Firstly, we establish the local well-posedness for the integral form of the (HS) equation by constructing some special spaces , which mix Lebesgue spaces and homogeneous Besov spaces. Then we present a global existence result and provide a sufficient condition for strong solutions to blow up in finite time for the equation. Finally, we give the ill-posedness and the unique continuation of the Hunter-Saxton equation.
Cite
@article{arxiv.2012.15429,
title = {On the Cauchy problem for the Hunter-Saxton equation on the line},
author = {Weikui Ye and Zhaoyang Yin},
journal= {arXiv preprint arXiv:2012.15429},
year = {2021}
}