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Lipschitz metric for the Hunter-Saxton equation. (English) Zbl 1195.35046
Summary: We study stability of solutions of the Cauchy problem for the Hunter-Saxton equation $u_t + uu_x = \frac 14 (\int^x_{-\infty} u^2_x dx)$ with initial data $u_{0}$. In particular, we derive a new Lipschitz metric $d_{\cal D}$ with the property that for two solutions $u$ and $v$ of the equation we have $d_{\cal D} (u(t),v(t)) \leqslant e^{C^t} d_{\cal D} (u_0,v_0)$.

MSC:
35B35Stability of solutions of PDE
35R09Integro-partial differential equations
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References:
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