On the existence of global weak solutions to an integrable two-component Camassa–Holm shallow-water system
2013 ◽
Vol 56
(3)
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pp. 755-775
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AbstractIn this paper, we investigate the existence of global weak solutions to an integrable two-component Camassa–Holm shallow-water system, provided the initial datau0(x)andρ0(x)have end statesu± andρ±, respectively. By perturbing the Cauchy problem of the system around rarefaction waves of the well-known Burgers equation, we obtain a global weak solution for the system under the assumptionsu− ≤ u+andρ− ≤ ρ+.
2011 ◽
Vol 260
(4)
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pp. 1132-1154
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2010 ◽
Vol 11
(5)
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pp. 4164-4173
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2009 ◽
Vol 19
(03)
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pp. 477-499
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2011 ◽
Vol 251
(12)
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pp. 3558-3582
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2016 ◽
Vol 260
(12)
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pp. 8403-8427
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2011 ◽
Vol 52
(3)
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pp. 033507
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2019 ◽
Vol 267
(4)
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pp. 2531-2559
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