A Lipschitz metric for conservative solutions of the two-component Hunter--Saxton system
Anders Nordli
TL;DR
This paper proves the existence of conservative solutions for the two-component Hunter--Saxton system and introduces a Lipschitz metric to analyze their stability, advancing understanding of this nonlinear PDE.
Contribution
It establishes the existence of conservative solutions and constructs a Lipschitz metric for stability analysis, which is a novel approach for this system.
Findings
Existence of conservative solutions on the line.
Construction of a Lipschitz metric for stability.
Enhanced understanding of solution stability.
Abstract
We establish the existence of conservative solutions of the initial value problem of the two-component Hunter--Saxton system on the line. Furthermore we investigate the stability of these solutions by constructing a Lipschitz metric.
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