Global existence for the critical generalized KdV equation

DOI10.1090/S0002-9939-02-06871-5zbMath1034.35121OpenAlexW1480735531MaRDI QIDQ4794585

Felipe Linares, Gustavo Ponce, Germán E. Fonseca

Publication date: 19 February 2003

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-02-06871-5

zbMATH Keywords

generalized Korteweg-de Vries equationsolitary wave solutionexistence of global solutions in Sobolev spaces

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45)

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Cites Work

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• Global wellposedness for KdV below \(L^2\)
• Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation
• Existence of blow-up solutions in the energy space for the critical generalized KdV equation
• Lyapunov stability of ground states of nonlinear dispersive evolution equations
• Global well-posedness for the modified korteweg-de vries equation
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• Global well-posedness for semi-linear wave equations
• Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
• On the Ill-Posedness of the IVP for the Generalized Korteweg-De Vries and Nonlinear Schrödinger Equations
• Instability of solitons for the critical generalized Korteweg-de Vries equation

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