October  2009, 23(4): 1295-1311. doi: 10.3934/dcds.2009.23.1295

Well-posedness in $ H^1 $ for generalized Benjamin-Ono equations on the circle

1. 

L.A.G.A., Institut Galilée, Université Paris-Nord, 93430 Villetaneuse, France

2. 

Université de Marne–La–Vallée, Equipe d’Analyse et de Mathématiques Appliquées, 5 bd. Descartes, Cité Descartes, Champs-sur-Marne, 77454 Marne-La-Vallée Cedex 2, France

Received  June 2007 Revised  April 2008 Published  November 2008

We prove the local-well posedness of the generalized Benjamin-Ono equations in $ H^1(\T) $.
Citation: Luc Molinet, Francis Ribaud. Well-posedness in $ H^1 $ for generalized Benjamin-Ono equations on the circle. Discrete & Continuous Dynamical Systems - A, 2009, 23 (4) : 1295-1311. doi: 10.3934/dcds.2009.23.1295
[1]

G. Fonseca, G. Rodríguez-Blanco, W. Sandoval. Well-posedness and ill-posedness results for the regularized Benjamin-Ono equation in weighted Sobolev spaces. Communications on Pure & Applied Analysis, 2015, 14 (4) : 1327-1341. doi: 10.3934/cpaa.2015.14.1327

[2]

Francis Ribaud, Stéphane Vento. Local and global well-posedness results for the Benjamin-Ono-Zakharov-Kuznetsov equation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (1) : 449-483. doi: 10.3934/dcds.2017019

[3]

Dongfeng Yan. KAM Tori for generalized Benjamin-Ono equation. Communications on Pure & Applied Analysis, 2015, 14 (3) : 941-957. doi: 10.3934/cpaa.2015.14.941

[4]

Jerry Bona, H. Kalisch. Singularity formation in the generalized Benjamin-Ono equation. Discrete & Continuous Dynamical Systems - A, 2004, 11 (1) : 27-45. doi: 10.3934/dcds.2004.11.27

[5]

Amin Esfahani, Steve Levandosky. Solitary waves of the rotation-generalized Benjamin-Ono equation. Discrete & Continuous Dynamical Systems - A, 2013, 33 (2) : 663-700. doi: 10.3934/dcds.2013.33.663

[6]

Yongye Zhao, Yongsheng Li, Wei Yan. Local Well-posedness and Persistence Property for the Generalized Novikov Equation. Discrete & Continuous Dynamical Systems - A, 2014, 34 (2) : 803-820. doi: 10.3934/dcds.2014.34.803

[7]

C. H. Arthur Cheng, John M. Hong, Ying-Chieh Lin, Jiahong Wu, Juan-Ming Yuan. Well-posedness of the two-dimensional generalized Benjamin-Bona-Mahony equation on the upper half plane. Discrete & Continuous Dynamical Systems - B, 2016, 21 (3) : 763-779. doi: 10.3934/dcdsb.2016.21.763

[8]

Sondre Tesdal Galtung. A convergent Crank-Nicolson Galerkin scheme for the Benjamin-Ono equation. Discrete & Continuous Dynamical Systems - A, 2018, 38 (3) : 1243-1268. doi: 10.3934/dcds.2018051

[9]

Boris Kolev. Local well-posedness of the EPDiff equation: A survey. Journal of Geometric Mechanics, 2017, 9 (2) : 167-189. doi: 10.3934/jgm.2017007

[10]

Luiz Gustavo Farah. Local solutions in Sobolev spaces and unconditional well-posedness for the generalized Boussinesq equation. Communications on Pure & Applied Analysis, 2009, 8 (5) : 1521-1539. doi: 10.3934/cpaa.2009.8.1521

[11]

Xi Tu, Zhaoyang Yin. Local well-posedness and blow-up phenomena for a generalized Camassa-Holm equation with peakon solutions. Discrete & Continuous Dynamical Systems - A, 2016, 36 (5) : 2781-2801. doi: 10.3934/dcds.2016.36.2781

[12]

Jaime Angulo, Carlos Matheus, Didier Pilod. Global well-posedness and non-linear stability of periodic traveling waves for a Schrödinger-Benjamin-Ono system. Communications on Pure & Applied Analysis, 2009, 8 (3) : 815-844. doi: 10.3934/cpaa.2009.8.815

[13]

Nakao Hayashi, Pavel Naumkin. On the reduction of the modified Benjamin-Ono equation to the cubic derivative nonlinear Schrödinger equation. Discrete & Continuous Dynamical Systems - A, 2002, 8 (1) : 237-255. doi: 10.3934/dcds.2002.8.237

[14]

Kenta Ohi, Tatsuo Iguchi. A two-phase problem for capillary-gravity waves and the Benjamin-Ono equation. Discrete & Continuous Dynamical Systems - A, 2009, 23 (4) : 1205-1240. doi: 10.3934/dcds.2009.23.1205

[15]

Lufang Mi, Kangkang Zhang. Invariant Tori for Benjamin-Ono Equation with Unbounded quasi-periodically forced Perturbation. Discrete & Continuous Dynamical Systems - A, 2014, 34 (2) : 689-707. doi: 10.3934/dcds.2014.34.689

[16]

Hartmut Pecher. Local well-posedness for the nonlinear Dirac equation in two space dimensions. Communications on Pure & Applied Analysis, 2014, 13 (2) : 673-685. doi: 10.3934/cpaa.2014.13.673

[17]

Jae Min Lee, Stephen C. Preston. Local well-posedness of the Camassa-Holm equation on the real line. Discrete & Continuous Dynamical Systems - A, 2017, 37 (6) : 3285-3299. doi: 10.3934/dcds.2017139

[18]

Zhaohui Huo, Boling Guo. The well-posedness of Cauchy problem for the generalized nonlinear dispersive equation. Discrete & Continuous Dynamical Systems - A, 2005, 12 (3) : 387-402. doi: 10.3934/dcds.2005.12.387

[19]

Jerry L. Bona, Laihan Luo. Large-time asymptotics of the generalized Benjamin-Ono-Burgers equation. Discrete & Continuous Dynamical Systems - S, 2011, 4 (1) : 15-50. doi: 10.3934/dcdss.2011.4.15

[20]

Vishal Vasan, Bernard Deconinck. Well-posedness of boundary-value problems for the linear Benjamin-Bona-Mahony equation. Discrete & Continuous Dynamical Systems - A, 2013, 33 (7) : 3171-3188. doi: 10.3934/dcds.2013.33.3171

2018 Impact Factor: 1.143

Metrics

  • PDF downloads (17)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]