Uniqueness of conservative solutions for the Hunter-Saxton equation

Abstract

We show that the Hunter-Saxton equation $u_t+u{u}_x=\frac{1}{4}({\int }_{-\infty }^{x}d\mu (t,z)-{\int }_x^{\infty }d\mu (t,z))$ and ${\mu }_t+(u\mu {)}_x=0$ has a unique, global, weak, and conservative solution $(u,\mu )$ of the Cauchy problem on the line.

arXiv comment54 pages

References in corpus (5)

• The Hunter-Saxton equation with noise
• A Lipschitz metric for the Hunter-Saxton equation
• Existence and Lipschitz stability for $\alpha$-dissipative solutions of the two-component Hunter-Saxton system
• Numerical conservative solutions of the Hunter--Saxton equation
• Lipschitz Stability for the Hunter-Saxton Equation