Lipschitz metric for the periodic Camassa-Holm equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:250

Article

Grunert, Katrin²  Holden, Helge^1,3  Raynaud, Xavier³ 

[1] Norwegian Univ Sci & Technol, Dept Math Sci, NO-7491 Trondheim, Norway

[2] Univ Vienna, Fac Math, A-1090 Vienna, Austria

[3] Univ Oslo, Ctr Math Applicat, NO-0316 Oslo, Norway

关键词: Camassa-Holm equation;    Lipschitz metric;    Conservative solutions;   

DOI  :  10.1016/j.jde.2010.07.006

来源: Elsevier

【 摘 要 】

We study the stability of conservative solutions of the Cauchy problem for the Camassa-Holm equation u(t) - u(xxt) + kappa u(x) + 3uu(x) - 2u(x)u(xx) - uu(xxx) = 0 with periodic initial data u(0). In particular. we derive a new Lipschitz metric d(D) with the property that for two solutions u and v of the equation we have d(D)(u(t), v(t)) <= e(Ct)d(D)(u(0), v(0)). The relationship between this metric and usual norms in H-per(1) and L-per(infinity) is clarified. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free