Courant Institute of Mathematical Sciences
Mathematics Colloquium
February 25, 2013
Speaker: Helge Holden, Norwegian University of Science and Technology, Norway
Title: The Camassa-Holm Equation --- A Survey
Abstract:
The Camassa-Holm equation u_t-u_{xxt}+ u_x+3u u_x-2u_x u_{xx}-u u_{xxx}=0 has
received considerable attention the last 20 years due to its many intriguing mathematical
properties. In particular, the Cauchy problem possesses two distinct classes of
solutions due to the wave breaking of the solution. We review the current understanding
of this problem, with emphasis on the Lipschitz stability of the solution of the Cauchy
problem. Extensions to a two-component generalization of the Camassa-Holm equation
will also be discussed. The talk is based on joint work with X. Raynaud (University of
Oslo) and K. Grunert (Norwegian University of Science and Technology).