Global Weak Solutions for a Shallow Water Equation

By Adrian Constantin, Luc Molinet. 2000

335 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f2fdb1bc8cf4d5d45dad5a7c320f1dc4cbf8447e

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In Applied Mathematics

1. Yue Liu
2. Zhaoyang Yin
3. Joachim Escher
4. Weipeng Zhu
5. Yanghai Yu
6. Jinlu Li
7. David Henry
8. Yong Zhou

In Mathematical Physics

1. Zhaoyang Yin
2. Yue Liu
3. Joachim Escher
4. Yong Zhou
5. Helge Holden
6. Xavier Raynaud
7. David Henry
8. Jinlu Li

In Statistical and Nonlinear Physics

1. Zhaoyang Yin
2. Yue Liu
3. Helge Holden
4. Xavier Raynaud
5. Joachim Escher
6. Yong Zhou
7. David Henry
8. Jinlu Li

Citations in the corpus

• Non-uniform dependence on initial data for the Camassa-Holm equation in Besov spaces (2020, background): “The existence and uniqueness of global weak solutions to the CH equation were proved in [16, 32].”
• Infinite propagation speed for a two component Camassa-Holm equation (2009, background): “Some solutions exist globally, whereas others exist only for a finite length of time, modelling wave breaking [5, 8, 12, 21, 22 ].”
• Global weak solutions and blow-up structure for the Degasperis–Procesi equation (2006, background): “The following notion was introduced in [12], see also [54].”
• Shock waves and blow-up phenomena for the periodic Degasperis-Procesi equation (2007, background): “On the other hand, it has global weak solutions with initial data u0 ∈ H1 [2, 11, 16, 44].”
• An Optimal Transportation Metric for Solutions of the Camassa-Holm Equation (2005, background): “l integro-differential term: ut+(u2/2)x+Px= 0, (1.1) where Pis defined as a convolution: P . = 1 2 e−|x| ∗ u2 + u2 x 2 . (1.2) For the physical motivations of this equation we refer to [CH], [CM1], [CM2], [J]. Earlier results on the existence and uniqueness of solutions can be found in [XZ1], [XZ2].”
• Blow-up of solutions to a nonlinear dispersive rod equation (2006, background): “However, In [24, 25], global existence of weak solutions is proved but uniqueness is obtained only under an a priori assumption that is known to hold only for initial data u0(x) ∈ H 1 such that u0 − u0 xx is a sign-definite Radon measure (under this condition, global existence and uniqueness was sho”
• 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].”
• On the Cauchy Problem of the Camassa-Holm Equation (2006, background): “In particular, it was proved in [ 16 ] that (2) with initial data m0(x)=u0(x) u0xx(x) is globally well-posed in Hp 2 if m0(x)2Hp 2 does not change sign.”
• Blow-up of solutions to the DGH equation (2007, background): “However, in [36], global existence of weak solutions is proved but uniqueness is obtained only under an a priori assumption that is known to hold only for initial data u0(x) ∈H 1 such that u0 − u0xx is a sign-definite Radon measure (under this condition, global existence and uniqueness was shown in ”
• Global existence and blow-up solutions for a nonlinear shallow water equation (2006, background): “[CaHo,BeSaSz, CoMo2 ] and are orbitally stable [CoMo,CoSt1], breaking waves occur [CaHo,Co1,Mc], and global solutions exist[Co1,CoEs].”