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Communications in Partial Differential Equations Volume 28, 2003 - Issue 11-12
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Original Articles

On the Cauchy Problem for the Generalized Korteweg-de Vries Equation

Luc Molinet L.A.G.A., Institut Galilée, Université Paris 13, Villetaneuse, FranceCorrespondence[email protected]
&
Francis Ribaud Equipe d'Analyse et de Mathématiques Appliquées, Université de Marne-la-Vallée, Marne-la-Vallée, France
Pages 2065-2091 | Received 01 Oct 2002, Published online: 01 Sep 2006

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Zaiyun Zhang, Zhenhai Liu, Mingbao Sun & Songhua Li. (2018) Well-posedness and unique continuation property for the solutions to the generalized Kawahara equation below the energy space. Applicable Analysis 97:15, pages 2655-2685.
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Articles from other publishers (21)

Yufeng Lu. (2023) Well‐posedness of generalized KdV and one‐dimensional fourth‐order derivative nonlinear Schrödinger equations for data with an infinite L 2 norm . Studies in Applied Mathematics 150:3, pages 883-898.
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Zaiyun Zhang, Zhenhai Liu, Mingbao Sun & Songhua Li. (2018) Low Regularity for the Higher Order Nonlinear Dispersive Equation in Sobolev Spaces of Negative Index. Journal of Dynamics and Differential Equations 31:1, pages 419-433.
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Jun-ichi Segata & Keishu Watanabe. (2016) The generalized Korteweg-de Vries equation with time oscillating nonlinearity in scale critical Sobolev space. Nonlinear Differential Equations and Applications NoDEA 23:5.
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Zaiyun Zhang & Jianhua Huang. (2016) Well-posedness and unique continuation property for the generalized Ostrovsky equation with low regularity. Mathematical Methods in the Applied Sciences 39:10, pages 2488-2513.
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Satoshi Masaki & Jun-ichi Segata. (2016) On the well-posedness of the generalized Korteweg–de Vries equation in scale-critical Lr-space. Analysis & PDE 9:3, pages 699-725.
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Herbert Koch. (2015) Self-similar solutions to super-critical gKdV. Nonlinearity 28:3, pages 545-575.
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Herbert Koch. 2014. Singular Phenomena and Scaling in Mathematical Models. Singular Phenomena and Scaling in Mathematical Models 49 67 .
Nils Strunk. (2013) Well-posedness for the supercritical gKdV equation. Communications on Pure and Applied Analysis 13:2, pages 527-542.
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Wei Yan, Yongsheng Li & Xingyu Yang. (2011) The Cauchy problem for the modified Kawahara equation in Sobolev spaces with low regularity. Mathematical and Computer Modelling 54:5-6, pages 1252-1261.
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Suxia Xia & Guixiang Xu. (2011) On the Cauchy problem for the NLS equations in. Applied Mathematics and Computation 217:19, pages 7737-7752.
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Wei Yan & Yongsheng Li. (2010) The Cauchy problem for Kawahara equation in Sobolev spaces with low regularity. Mathematical Methods in the Applied Sciences 33:14, pages 1647-1660.
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Didier Pilod. (2008) On the Cauchy problem for higher-order nonlinear dispersive equations. Journal of Differential Equations 245:8, pages 2055-2077.
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Lijia Han & Baoxiang Wang. (2008) Global wellposedness and limit behavior for the generalized finite-depth-fluid equation with small data in critical Besov spaces . Journal of Differential Equations 245:8, pages 2103-2144.
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Ruying Xue. (2008) THE INITIAL-BOUNDARY-VALUE PROBLEM OF A GENERALIZED BOUSSINESQ EQUATION ON THE HALF LINE. Journal of the Korean Mathematical Society 45:1, pages 79-95.
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Gui-xiang Xu. (2007) The Cauchy Problem of the Nonlinear Schrödinger Equations in ℝ1+1. Acta Mathematicae Applicatae Sinica, English Series 23:4, pages 593-610.
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Baoxiang Wang & Chunyan Huang. (2007) Frequency-uniform decomposition method for the generalized BO, KdV and NLS equations. Journal of Differential Equations 239:1, pages 213-250.
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Ai Guo & Shangbin Cui. (2007) On the Cauchy problem of fourth-order nonlinear Schrödinger equations. Nonlinear Analysis: Theory, Methods & Applications 66:12, pages 2911-2930.
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Baoxiang Wang & Henryk Hudzik. (2007) The global Cauchy problem for the NLS and NLKG with small rough data. Journal of Differential Equations 232:1, pages 36-73.
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Ai Guo & Shangbin Cui. (2006) Solvability of the Cauchy problem of nonlinear beam equations in Besov spaces. Nonlinear Analysis: Theory, Methods & Applications 65:4, pages 802-824.
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Ruying Xue. (2006) Local and global existence of solutions for the Cauchy problem of a generalized Boussinesq equation. Journal of Mathematical Analysis and Applications 316:1, pages 307-327.
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Luc Molinet & Francis Ribaud. (2003) On the Cauchy problem for the generalized Benjamin–Ono equation with small initial data. Comptes Rendus Mathematique 337:8, pages 523-526.
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