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Preprint 2006-001

Global Conservative Solutions of the Camassa–Holm Equation – A Lagrangian Point of View

Helge Holden and Xavier Raynaud

Abstract: We show that the Camassa–Holm equation ut−uxxt+3uux−2uxuxx−uuxxx=0 possesses a global continuous semigroup of weak conservative solutions for initial data u|t=0 in H1. The result is obtained by introducing a coordinate transformation into Lagrangian coordinates. To characterize conservative solutions it is necessary to include the energy density given by the positive Radon measure μ with μac=(u2+ux2)dx.

Paper:
Available as PDF (360 Kbytes).
Author(s):
Helge Holden,
Xavier Raynaud,
Publishing information:
Comments:
See also 2006-011
Submitted by:
; 2006-03-02.