Global Solutions of the Hunter--Saxton Equation

2005/01/01 by Alberto Bressan, Adrian Constantin · 174 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Applied mathematics #Construct (python library) #Dissipative system #First-order partial differential equation #Liquid crystal #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Nonlinear system #Partial differential equation #Physics #Quantum chaos and dynamical systems #Semigroup #Thermodynamics

paper · doi:10.1137/050623036

published in SIAM Journal on Mathematical Analysis 37(3), 996-1026 (Society for Industrial and Applied Mathematics)

openalex publication_date 2005/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08

Abstract

We construct a continuous semigroup of weak, dissipative solutions to a nonlinear partial differential equation modeling nematic liquid crystals. A new distance functional, determined by a problem of optimal transportation, yields sharp estimates on the continuity of solutions with respect to the initial data.

Citations

• Inverse scattering solutions of the hunter-saxton equation
• Topics in Optimal Transportation
• Camassa–Holm, Korteweg–de Vries and related models for water waves
• On a nonlinear hyperbolic variational equation: I. Global existence of weak solutions
• Dynamics of Director Fields
• On a nonlinear hyperbolic variational equation: II. The zero-viscosity and dispersion limits
• Euler equations on homogeneous spaces and Virasoro orbits
• The Camassa–Holm equation as a geodesic flow on the diffeomorphism group
• Wave breaking for nonlinear nonlocal shallow water equations
• Existence of permanent and breaking waves for a shallow water equation: a geometric approach
• Geodesic flow on the diffeomorphism group of the circle
• Transformations for the Camassa-Holm Equation, Its High-Frequency Limit and the Sinh-Gordon Equation

Cited by

• Orientation waves in a director field with rotational inertia
• Hunter–Saxton equation [wikipedia]