The Camassa-Holm equation, proof of existence of solutions.
DIFTA 2005–03–17 and 2005–03–31?
Abstract:
I will present results contained in the following papers:
- Xin Zhouping, Zhang Ping,
On the weak solutions to a shallow water equation.
Comm. Pure Appl. Math. 53 (2000), no. 11,
1411–1433
- Giuseppe M. Coclite, Helge Holden and Kenneth H. Karlsen,
Wellposedness for a parabolic-elliptic system.
Preprint.
- Giuseppe M. Coclite, Helge Holden and Kenneth H. Karlsen,
Global weak solutions to a generalized hyperelastic-rod wave equation.
Preprint.
I think I will need 4 hours. The first
two hours will be dedicated to the proof of
existence of viscous regularization. This method
is quite general and is used in conservation
laws. During the two remaining hours, I will let
the viscosity tend to zero and prove that there
exists a subsequence that converges to the
solution of the Camassa-Holm equation.