A Lipschitz metric for the Camassa–Holm equation

Abstract: The Camassa—Holm equation u_t+uu_x+p_x= 0, p−p_{xx}=u^2+1/2u_x^2 has received considerable attention since it was first studied by Camassa andHolm in 1993. Part of the interest stems from the fact that the solution developssingularities in finite time while keeping theH1norm finite. At wave breakinguniqueness is lost as the there are infinitely many ways to extend the solutionbeyond wave breaking. We study the so-called conservative solutions and showhow to construct a Lipschitz metric comparing two conservative solutions.This is joint work with J. A. Carrillo (Imperial) and K. Grunert (NTNU).

analysis of PDEsdynamical systemsfunctional analysisoptimization and controlspectral theory

Audience: advanced learners

Webinar on PDE and related areas

Series comments: The webinar is organised jointly from IIT-Kanpur, TIFR-CAM,Bangalore, IISER-Pune and IISER-Kolkata.

Zoom Link for the talk will be available on iitk.ac.in/math/weekly-webinar-on-pde-and-related-areas

If you would like to receive webinar announcements(including zoom ID and password to attend the talk), please send a blank email with the subject line "WWOPARA_sub" to pdewebinar@iitk.ac.in. In order to unsubscribe, please send us a blank email with the subject "WWOPARA_unsub".