A CONTINUOUS INTERPOLATION BETWEEN CONSERVATIVE AND DISSIPATIVE SOLUTIONS FOR THE TWO-COMPONENT CAMASSA-HOLM SYSTEM

被引：23
作者：
Grunert, Katrin [1 ,2 ]
Holden, Helge [2 ,3 ]
Raynaud, Xavier [2 ,4 ]
机构：
[1] Norwegian Univ Sci & Technol, Dept Math Sci, NO-7491 Trondheim, Norway
[2] Norwegian Univ Sci & Technol, Dept Math Sci, NO-7491 Trondheim, Norway
[3] Univ Oslo, Ctr Math Applicat, NO-0316 Oslo, Norway
[4] SINTEF ICT, Appl Math, NO-0314 Oslo, Norway
来源：
FORUM OF MATHEMATICS SIGMA | 2015年 / 3卷
基金：
奥地利科学基金会;
关键词：
D O I：
10.1017/fms.2014.29
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We introduce a novel solution concept, denoted alpha-dissipative solutions, that provides a continuous interpolation between conservative and dissipative solutions of the Cauchy problem for the two-component Camassa-Holm system on the line with vanishing asymptotics. All the alpha-dissipative solutions are global weak solutions of the same equation in Eulerian coordinates, yet they exhibit rather distinct behavior at wave breaking. The solutions are constructed after a transformation into Lagrangian variables, where the solution is carefully modified at wave breaking.
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页数：73
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