Towards well-posedness of the L^2-metric on the space of curves
Event details
| Date | 29.10.2014 |
| Hour | 16:30 › 17:30 |
| Speaker | Martins Bruveris (Brunel) |
| Location |
GR A3 30
|
| Category | Conferences - Seminars |
Geometry and Dynamics Seminar
Abstract: I will discuss the technique employed in [1], where Euler's equation was approximated by relaxing the incompressibility constraint and considering geodesic equations of higher order Sobolev metrics on the group of all (compressible) diffeomorphisms. Euler's equations were recovered as the limiting case of this family of equations and it was shown that solutions of this family converge to solutions to Euler's equation.
In the second part of the talk I will discuss using the technique to view the L^2-metric on the space of curves as the limiting case of higher order Sobolev metrics and thus hopefully establishing the well-posedness of the geodesic equation for the L^2-metric.
[1] Mumford & Michor: On Euler's equation and 'EPDiff'. J. Geom. Mech. 5(3), 319-344, 2013.
Abstract: I will discuss the technique employed in [1], where Euler's equation was approximated by relaxing the incompressibility constraint and considering geodesic equations of higher order Sobolev metrics on the group of all (compressible) diffeomorphisms. Euler's equations were recovered as the limiting case of this family of equations and it was shown that solutions of this family converge to solutions to Euler's equation.
In the second part of the talk I will discuss using the technique to view the L^2-metric on the space of curves as the limiting case of higher order Sobolev metrics and thus hopefully establishing the well-posedness of the geodesic equation for the L^2-metric.
[1] Mumford & Michor: On Euler's equation and 'EPDiff'. J. Geom. Mech. 5(3), 319-344, 2013.
Practical information
- Expert
- Free
Organizer
- Sonja Hohloch