The global solvability of the Kirchhoff equation with Sobolev data
Analysis of PDEs
2022-09-07 v3 Functional Analysis
Abstract
We consider linear and non-linear Cauchy equations in the context of Sobolev spaces. In particular, we show the global existence of solutions to the Kirchhoff equation with initial data in the Sobolev spaces, a problem that has been open for more than eighty years. Our proof is based on a new uniform estimate for solutions to the linear equation with time-dependent coefficient and a fixed point argument. As an immediate consequence of our result, the global solvability of the Kirchhoff equation with initial data in the Gevrey spaces is also obtained.
Keywords
Cite
@article{arxiv.2207.02076,
title = {The global solvability of the Kirchhoff equation with Sobolev data},
author = {Tokio Matsuyama and Lenny Neyt},
journal= {arXiv preprint arXiv:2207.02076},
year = {2022}
}
Comments
Due to an error in the proof of Theorem 2.2, it is unsure if any of the subsequent results are correct