Lipschitz Stability for the Hunter-Saxton Equation

Abstract

We study the Lipschitz stability in time for $\alpha$-dissipative solutions to the Hunter-Saxton equation, where $\alpha \in [0,1]$ is a constant. We define metrics in both Lagrangian and Eulerian coordinates, and establish Lipschitz stability for those metrics.

Third Version: Corrected some typos and small mistakes noticed after submission. Added a missing condition in the definition of the set of Eulerian coordinates

Cited by in corpus (4)

• Uniqueness of conservative solutions for the Hunter-Saxton equation
• A Convergent Numerical Algorithm for $\alpha$-Dissipative Solutions of the Hunter-Saxton Equation
• A Lipschitz metric for $\alpha$-dissipative solutions to the Hunter-Saxton equation
• A numerical view on α-dissipative solutions of the Hunter-Saxton equation