Global Conservative Solutions of the Camassa–Holm Equation

By Alberto Bressan, Adrian Constantin. 2007

888 citations recorded by the source corpus.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/92224fe37bb5f2be0c766f3f43e1947198e1f511

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Yue Liu
2. Zhaoyang Yin
3. Helge Holden
4. Xavier Raynaud
5. Lorenzo Brandolese
6. Carlos E. Kenig
7. A. Alexandrou Himonas
8. Yong Zhou

In Statistical and Nonlinear Physics

1. Yue Liu
2. Zhaoyang Yin
3. Changzheng Qu
4. A. Alexandrou Himonas
5. Lorenzo Brandolese
6. Yong Zhou
7. Helge Holden
8. Carlos E. Kenig

Citations in the corpus

• Global weak solutions for a two-component Camassa–Holm shallow water system (2011, background): “On the other hand, it has global weak solutions in H 1(R) [2,3,15,22,47].”
• A three-component generalization of Camassa–Holm equation with N-peakon solutions (2011, background): “4) have to be interpreted in the weak sense [33,28,6].”
• Global Existence and Blow-Up Phenomena for the Degasperis-Procesi Equation (2006, background): “On the other hand, it has global weak solutions in H 1 (R) [ 2 , 12, 15, 46].”
• Dissipative solutions for the Camassa-Holm equation (2009, background): “The problem of continuation beyond wave breaking has been considered by Bressan and Constantin [3] [4] and Holden and Raynaud [22].”
• Global Conservative Solutions of the Camassa–Holm Equation—A Lagrangian Point of View (2007, methodology): “This result is stronger than in Bressan and Constantin (2007) where it is proven that if ūn → u in H1 , then Tt un → u t in L .”
• Lipschitz metric for the Camassa-Holm equation on the line (2010, background): “We are interested in the latter case, for which solutions have been studied by Bressan and Constantin [1] and Holden and Raynaud [13, 14].”
• The local well-posedness and existence of weak solutions for a generalized Camassa-Holm equation (2010, background): “The sharpest results for the global existence and blow-up solutions are found in Bressan and Constantin [2,3].”
• Low-Regularity Solutions of the Periodic Camassa–Holm Equation (2007, result): “Further results in the H 1 setting have been recently proved in Bressan and Constantin ( 2005 ) and Bressan and Fonte ( 2005 ).”
• Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems (2016, neutral): “properties for CH type and related nonlinear evolution equations, we refer the reader to [12], [13], [11], [15], [16], [6], [23], [49], [53], [50], [17], [45], [8], [42], [43], [44], [4], [3], [64], [18], [5], [47], [48], [10], [9], [70], and the references therein.”
• Initial Boundary Value Problems of the Camassa–Holm Equation (2008, background): “On the other hand, it has global weak solutions in H1 I , cf. Bressan and Constantin (2007), Constantin and Molinet (2000), Danchin (2001), Molinet (2004), Wahlén (2006), and Xin and Zhang (2000).”