Lipschitz metric for the Hunter-Saxton equation

2009/04/23 by Helge Holden, Bressan, Alberto, Holden, Helge +1
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Advanced Mathematical Physics Problems #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.0904.3615

Abstract

We study stability of solutions of the Cauchy problem for the Hunter-Saxton equation u_t+uu_x=\frac14(∫_-∞^xu_x² dx-∫_x^∞ u_x² dx) with initial data u₀. In particular, we derive a new Lipschitz metric d_\D with the property that for two solutions u and v of the equation we have d_\D(u(t),v(t))≤ e^Ct d_\D(u₀,v₀).

Citations

• Global Conservative Solutions of the Camassa–Holm Equation

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