On initial boundary value problems for variants of the Hunter-Saxton equation

Abstract

The Hunter-Saxton equation serves as a mathematical model for orientation waves in a nematic liquid crystal. The present paper discusses a modified variant of this equation, coming up in the study of critical points for the speed of orientation waves, as well as a two-component extension. We establish well-posedness and blow-up results for some initial boundary value problems for the modified Hunter-Saxton equation and the two-component Hunter-Saxton system.

14 pages

References in corpus (5)

• On asymptotically equivalent shallow water wave equations
• Integrable evolution equations on spaces of tensor densities and their peakon solutions
• On the N=2 Supersymmetric Camassa-Holm and Hunter-Saxton Equations
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• The curvature of semidirect product groups associated with two-component Hunter-Saxton systems