The Hunter-Saxton system: more than a generalization
Event details
| Date | 18.03.2013 |
| Hour | 17:15 › 18:00 |
| Speaker | Marcus Wunsch, ETH Zürich |
| Location | |
| Category | Conferences - Seminars |
Hamiltonian Dynamics Seminar
Abstract: In this talk, I will review some recent work on the Hunter-Saxton system, subject to periodic boundary conditions. The Hunter-Saxton system is a generalization of the (single-component) Hunter-Saxton equation, which describes the propagation of weakly nonlinear orientation waves in a massive director field of a nematic liquid crystal. Moreover, the system (1) is the high-frequency limit of the two-component Camassa-Holm equation arising in the theory of shallow water waves, and it has also been proposed as a model for the nonlinear dynamics of dark matter. After preparing the analytic foundations for this coupled nonlinear system, I will prove that classical solutions to (1) have explicit representations in terms of their Lagrangian coordinates. The latter, it turns out, describe the geodesics on an infinite-dimensional sphere (κ = 1) or pseudosphere (κ = −1), which a posteriori reveals why there are explicit solution formulae. Finally, I will show how the geometric picture guides us naturally to the construction of weak solutions.
Abstract: In this talk, I will review some recent work on the Hunter-Saxton system, subject to periodic boundary conditions. The Hunter-Saxton system is a generalization of the (single-component) Hunter-Saxton equation, which describes the propagation of weakly nonlinear orientation waves in a massive director field of a nematic liquid crystal. Moreover, the system (1) is the high-frequency limit of the two-component Camassa-Holm equation arising in the theory of shallow water waves, and it has also been proposed as a model for the nonlinear dynamics of dark matter. After preparing the analytic foundations for this coupled nonlinear system, I will prove that classical solutions to (1) have explicit representations in terms of their Lagrangian coordinates. The latter, it turns out, describe the geodesics on an infinite-dimensional sphere (κ = 1) or pseudosphere (κ = −1), which a posteriori reveals why there are explicit solution formulae. Finally, I will show how the geometric picture guides us naturally to the construction of weak solutions.
Practical information
- Expert
- Free
Organizer
- Martins Bruveris, Sonja Hohloch