# Mathematics Colloquium

#### The Camassa-Holm Equation --- a Survey

**Speaker:**
Helge Holden, Norwegian University of Science and Technology, Norway

**Location:**
Warren Weaver Hall 1302

**Date:**
Monday, February 25, 2013, 3:45 p.m.

**Synopsis:**

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).