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Preprint 2010-008

Lipschitz metric for the periodic Camassa–Holm equation

Katrin Grunert, Helge Holden and Xavier Raynaud

Abstract: We study stability of conservative solutions of the Cauchy problem for the periodic Camassa–Holm equation ut−uxxt+3uux−2uxuxx−uuxxx=0 with initial data u0. In particular, we derive a new Lipschitz metric dD with the property that for two solutions u and v of the equation we have dD(u(t),v(t))≤eCtdD(u0,v0). The relationship between this metric and usual norms in H1per and L∞per is clarified.

Paper:
Available as PDF (392 Kbytes).
Author(s):
Katrin Grunert,
Helge Holden,
Xavier Raynaud,
Submitted by:
; 2010-05-19.
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Last modified: 2010-05-19 13:05 UTC