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Variational derivation of the CamassaHolm shallow water equation with nonzero vorticity
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Wellposedness and blowup phenomena for the 2component CamassaHolm equation
On unique continuation for the modified EulerPoisson equations
1.  Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, United States 
2.  Department of Mathematics, University of Notre Dame, Notre Dame, IN 465565683, United States 
3.  Department of Mathematics, University of New Orleans, New Orleans, LA 70148, United States 
[1] 
Jae Min Lee, Stephen C. Preston. Local wellposedness of the CamassaHolm equation on the real line. Discrete & Continuous Dynamical Systems, 2017, 37 (6) : 32853299. doi: 10.3934/dcds.2017139 
[2] 
Xi Tu, Zhaoyang Yin. Local wellposedness and blowup phenomena for a generalized CamassaHolm equation with peakon solutions. Discrete & Continuous Dynamical Systems, 2016, 36 (5) : 27812801. doi: 10.3934/dcds.2016.36.2781 
[3] 
Kai Yan, Zhaoyang Yin. Wellposedness for a modified twocomponent CamassaHolm system in critical spaces. Discrete & Continuous Dynamical Systems, 2013, 33 (4) : 16991712. doi: 10.3934/dcds.2013.33.1699 
[4] 
Zhaoyang Yin. Wellposedness and blowup phenomena for the periodic generalized CamassaHolm equation. Communications on Pure & Applied Analysis, 2004, 3 (3) : 501508. doi: 10.3934/cpaa.2004.3.501 
[5] 
Joachim Escher, Olaf Lechtenfeld, Zhaoyang Yin. Wellposedness and blowup phenomena for the 2component CamassaHolm equation. Discrete & Continuous Dynamical Systems, 2007, 19 (3) : 493513. doi: 10.3934/dcds.2007.19.493 
[6] 
Jinlu Li, Zhaoyang Yin. Wellposedness and blowup phenomena for a generalized CamassaHolm equation. Discrete & Continuous Dynamical Systems, 2016, 36 (10) : 54935508. doi: 10.3934/dcds.2016042 
[7] 
Peng Gao. Carleman estimates and Unique Continuation Property for 1D viscous CamassaHolm equation. Discrete & Continuous Dynamical Systems, 2017, 37 (1) : 169188. doi: 10.3934/dcds.2017007 
[8] 
Yu Gao, JianGuo Liu. The modified CamassaHolm equation in Lagrangian coordinates. Discrete & Continuous Dynamical Systems  B, 2018, 23 (6) : 25452592. doi: 10.3934/dcdsb.2018067 
[9] 
Wei Yan, Yimin Zhang, Yongsheng Li, Jinqiao Duan. Sharp wellposedness of the Cauchy problem for the rotationmodified KadomtsevPetviashvili equation in anisotropic Sobolev spaces. Discrete & Continuous Dynamical Systems, 2021 doi: 10.3934/dcds.2021097 
[10] 
Ying Fu, Changzheng Qu, Yichen Ma. Wellposedness and blowup phenomena for the interacting system of the CamassaHolm and DegasperisProcesi equations. Discrete & Continuous Dynamical Systems, 2010, 27 (3) : 10251035. doi: 10.3934/dcds.2010.27.1025 
[11] 
Baoyan Sun, KungChien Wu. Global wellposedness and exponential stability for the fermion equation in weighted Sobolev spaces. Discrete & Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021147 
[12] 
Luiz Gustavo Farah. Local solutions in Sobolev spaces and unconditional wellposedness for the generalized Boussinesq equation. Communications on Pure & Applied Analysis, 2009, 8 (5) : 15211539. doi: 10.3934/cpaa.2009.8.1521 
[13] 
Tadahiro Oh, Yuzhao Wang. On global wellposedness of the modified KdV equation in modulation spaces. Discrete & Continuous Dynamical Systems, 2021, 41 (6) : 29712992. doi: 10.3934/dcds.2020393 
[14] 
Wei Luo, Zhaoyang Yin. Local wellposedness in the critical Besov space and persistence properties for a threecomponent CamassaHolm system with Npeakon solutions. Discrete & Continuous Dynamical Systems, 2016, 36 (9) : 50475066. doi: 10.3934/dcds.2016019 
[15] 
Aiyong Chen, Xinhui Lu. Orbital stability of elliptic periodic peakons for the modified CamassaHolm equation. Discrete & Continuous Dynamical Systems, 2020, 40 (3) : 17031735. doi: 10.3934/dcds.2020090 
[16] 
Stephen Anco, Daniel Kraus. Hamiltonian structure of peakons as weak solutions for the modified CamassaHolm equation. Discrete & Continuous Dynamical Systems, 2018, 38 (9) : 44494465. doi: 10.3934/dcds.2018194 
[17] 
Ying Fu. A note on the Cauchy problem of a modified CamassaHolm equation with cubic nonlinearity. Discrete & Continuous Dynamical Systems, 2015, 35 (5) : 20112039. doi: 10.3934/dcds.2015.35.2011 
[18] 
Andrea Natale, FrançoisXavier Vialard. Embedding CamassaHolm equations in incompressible Euler. Journal of Geometric Mechanics, 2019, 11 (2) : 205223. doi: 10.3934/jgm.2019011 
[19] 
G. Fonseca, G. RodríguezBlanco, W. Sandoval. Wellposedness and illposedness results for the regularized BenjaminOno equation in weighted Sobolev spaces. Communications on Pure & Applied Analysis, 2015, 14 (4) : 13271341. doi: 10.3934/cpaa.2015.14.1327 
[20] 
Priscila Leal da Silva, Igor Leite Freire. An equation unifying both CamassaHolm and Novikov equations. Conference Publications, 2015, 2015 (special) : 304311. doi: 10.3934/proc.2015.0304 
2020 Impact Factor: 1.392
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