Global existence for the critical generalized KdV equation

Authors:
G. Fonseca, F. Linares and G. Ponce

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1847-1855

MSC (2000):
Primary 35Q53

DOI:
https://doi.org/10.1090/S0002-9939-02-06871-5

Published electronically:
November 6, 2002

MathSciNet review:
1955273

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Abstract | References | Similar Articles | Additional Information

Abstract: We discuss results regarding global existence of solutions for the critical generalized Korteweg-de Vries equation,

The theory established shows the existence of global solutions in Sobolev spaces with order below the one given by the energy space , i.e. solutions corresponding to data , , with , where is the solitary wave solution of the equation.

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Additional Information

**G. Fonseca**

Affiliation:
Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia

Email:
gfonseca@matematicas.unal.edu.co

**F. Linares**

Affiliation:
Instituto de Matemática Pura e Aplicada, 22460-320, Rio de Janeiro, Brazil

Email:
linares@impa.br

**G. Ponce**

Affiliation:
Department of Mathematics, University of California, Santa Barbara, California 93106

Email:
ponce@math.ucsb.edu

DOI:
https://doi.org/10.1090/S0002-9939-02-06871-5

Received by editor(s):
January 30, 2002

Published electronically:
November 6, 2002

Additional Notes:
The first author was partially supported by DIB-Universidad Nacional de Colombia

The second author was partially supported by CNP-q Brazil

The third author was partially supported by an NSF grant

Communicated by:
David S. Tartakoff

Article copyright:
© Copyright 2002
American Mathematical Society