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Lipschitz metric for the periodic Camassa-Holm equation |
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| Authors: | Katrin Grunert Helge Holden Xavier Raynaud |
| Institution: | a Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, A-1090 Wien, Austria b Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway c Centre of Mathematics for Applications, University of Oslo, NO-0316 Oslo, Norway |
| Abstract: | We study the stability of conservative solutions of the Cauchy problem for the Camassa-Holm equation ut−uxxt+κux+3uux−2uxuxx−uuxxx=0 with periodic 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  and  is clarified. |
| Keywords: | primary 35Q53 35B35 secondary 35B20 |
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