Global well-posedness of Kirchhoff systems

TL;DR

This paper proves the global well-posedness in the H^1 space for Kirchhoff systems using asymptotic integrations, expanding understanding of solution existence for less regular data and providing practical examples.

Contribution

It introduces a novel approach based on asymptotic integrations for strictly hyperbolic systems to establish global well-posedness of Kirchhoff systems.

Findings

Established H^1 global well-posedness for Kirchhoff systems

Developed a new solution construction method using asymptotic integrations

Discussed solutions for less regular initial data and provided applications

Abstract

The aim of this paper is to establish the $H^1$ global well-posedness for Kirchhoff systems. The new approach to the construction of solutions is based on the asymptotic integrations for strictly hyperbolic systems with time-dependent coefficients. These integrations play an important role to setting the subsequent fixed point argument. The existence of solutions for less regular data is discussed, and several examples and applications are presented.