Recent Progress on the Global Well-Posedness of the KPI Equation

DOI10.1007/978-0-8176-4588-5_9zbMath1193.35191OpenAlexW14833992MaRDI QIDQ3566001

Carlos E. Kenig

Publication date: 7 June 2010

Published in: Recent Developments in Real and Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-0-8176-4588-5_9

zbMATH Keywords

energy spaceglobal well-posednessKPI equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

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• Global well-posedness of the KP-I initial-value problem in the energy space
• Erratum to ``Well-posedness and scattering for the KP-II equation in a critical space [Ann. I. H. Poincaré - AN 26 (3) (2009) 917-941]
• Local well posedness for modified Kadomstev-Petviashvili equations.
• On the Cauchy problem for the Kadomtsev-Petviashvili equation
• Well-posedness and ill-posedness results for the Kadomtsev-Petviashvili-I equation
• Correction: ``Global well-posedness for the KP-I equation
• On the local and global well-posedness theory for the KP-I equation
• Global well-posedness for the KP-I equation
• On finite energy solutions of the KP-I equation
• A priori bounds and weak solutions for the nonlinear Schrödinger equation in Sobolev spaces of negative order
• On equations of KP-type
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• A Priori Bounds for the 1D Cubic NLS in Negative Sobolev Spaces

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