Journal
COMMUNICATIONS IN MATHEMATICAL SCIENCES
Volume 14, Issue 6, Pages 1581-1597Publisher
INT PRESS BOSTON, INC
DOI: 10.4310/CMS.2016.v14.n6.a6
Keywords
Camassa-Holm equation; uniqueness; singularity; large data; characteristic
Categories
Funding
- NSFC [11201503]
- Fundamental Research Funds for the Central Universities [2014MDLXYXJ02]
- State Scholarship Fund, Scholarship Council of China
- NSF [DMS-1411786]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1411786] Funding Source: National Science Foundation
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The paper is concerned with a direct proof the uniqueness of global conservative solutions to the two-component Camassa-Holm system, based on characteristics. Given a conservative solution u= u(t, x) and rho=rho(t, x), an equation is introduced to single out a unique characteristic curve through each initial point. It is proved that the Cauchy problem with general initial data u(0) is an element of H-1(R), rho(0) is an element of L-2(R) has a unique global conservative solution.
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