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On the existence of quasi periodic and almost periodic solutions of neutral functional differential equations
Existence of the global attractor for weakly damped, forced KdV equation on Sobolev spaces of negative index
1.  Institut des Hautes Etudes Scientifiques, Le BoisMarie, 35, route de Chartres, 91440 BuressurYvette, France 
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S. Raynor, G. Staffilani. Low regularity stability of solitons for the KDV equation. Communications on Pure and Applied Analysis, 2003, 2 (3) : 277296. doi: 10.3934/cpaa.2003.2.277 
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J. Colliander, A. D. Ionescu, C. E. Kenig, Gigliola Staffilani. Weighted lowregularity solutions of the KPI initialvalue problem. Discrete and Continuous Dynamical Systems, 2008, 20 (2) : 219258. doi: 10.3934/dcds.2008.20.219 
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Takamori Kato. Global wellposedness for the Kawahara equation with low regularity. Communications on Pure and Applied Analysis, 2013, 12 (3) : 13211339. doi: 10.3934/cpaa.2013.12.1321 
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Wided Kechiche. Regularity of the global attractor for a nonlinear Schrödinger equation with a point defect. Communications on Pure and Applied Analysis, 2017, 16 (4) : 12331252. doi: 10.3934/cpaa.2017060 
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Felipe Linares, M. Panthee. On the Cauchy problem for a coupled system of KdV equations. Communications on Pure and Applied Analysis, 2004, 3 (3) : 417431. doi: 10.3934/cpaa.2004.3.417 
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Bassam Kojok. Global existence for a forced dispersive dissipative equation via the Imethod. Communications on Pure and Applied Analysis, 2009, 8 (4) : 14011419. doi: 10.3934/cpaa.2009.8.1401 
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V. Varlamov, Yue Liu. Cauchy problem for the Ostrovsky equation. Discrete and Continuous Dynamical Systems, 2004, 10 (3) : 731753. doi: 10.3934/dcds.2004.10.731 
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Adrien Dekkers, Anna RozanovaPierrat. Cauchy problem for the Kuznetsov equation. Discrete and Continuous Dynamical Systems, 2019, 39 (1) : 277307. doi: 10.3934/dcds.2019012 
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Takafumi Akahori. Low regularity global wellposedness for the nonlinear Schrödinger equation on closed manifolds. Communications on Pure and Applied Analysis, 2010, 9 (2) : 261280. doi: 10.3934/cpaa.2010.9.261 
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Oleksiy V. Kapustyan, Pavlo O. Kasyanov, José Valero. Structure and regularity of the global attractor of a reactiondiffusion equation with nonsmooth nonlinear term. Discrete and Continuous Dynamical Systems, 2014, 34 (10) : 41554182. doi: 10.3934/dcds.2014.34.4155 
[12] 
Abdelghafour Atlas. Regularity of the attractor for symmetric regularized wave equation. Communications on Pure and Applied Analysis, 2005, 4 (4) : 695704. doi: 10.3934/cpaa.2005.4.695 
[13] 
Cedric Galusinski, Serguei Zelik. Uniform Gevrey regularity for the attractor of a damped wave equation. Conference Publications, 2003, 2003 (Special) : 305312. doi: 10.3934/proc.2003.2003.305 
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Rudong Zheng, Zhaoyang Yin. The Cauchy problem for a generalized Novikov equation. Discrete and Continuous Dynamical Systems, 2017, 37 (6) : 35033519. doi: 10.3934/dcds.2017149 
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Roman Chapko, B. Tomas Johansson. An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semiinfinite regions. Inverse Problems and Imaging, 2008, 2 (3) : 317333. doi: 10.3934/ipi.2008.2.317 
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Jonathan Bennett. A trilinear restriction problem for the paraboloid in R^3. Electronic Research Announcements, 2004, 10: 97102. 
[17] 
Andreia Chapouto. A remark on the wellposedness of the modified KdV equation in the FourierLebesgue spaces. Discrete and Continuous Dynamical Systems, 2021, 41 (8) : 39153950. doi: 10.3934/dcds.2021022 
[18] 
Gerard Gómez, Josep–Maria Mondelo, Carles Simó. A collocation method for the numerical Fourier analysis of quasiperiodic functions. I: Numerical tests and examples. Discrete and Continuous Dynamical Systems  B, 2010, 14 (1) : 4174. doi: 10.3934/dcdsb.2010.14.41 
[19] 
Jianhua Huang, Yanbin Tang, Ming Wang. Singular support of the global attractor for a damped BBM equation. Discrete and Continuous Dynamical Systems  B, 2021, 26 (10) : 53215335. doi: 10.3934/dcdsb.2020345 
[20] 
Biyue Chen, Chunxiang Zhao, Chengkui Zhong. The global attractor for the wave equation with nonlocal strong damping. Discrete and Continuous Dynamical Systems  B, 2021, 26 (12) : 62076228. doi: 10.3934/dcdsb.2021015 
2020 Impact Factor: 1.916
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