Global existence for the critical generalized KdV equation
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- by G. Fonseca, F. Linares and G. Ponce PDF
- Proc. Amer. Math. Soc. 131 (2003), 1847-1855 Request permission
Abstract:
We discuss results regarding global existence of solutions for the critical generalized Korteweg-de Vries equation, \[ u_t+u_{xxx}+u^4 u_x=0,\quad x, t\in \mathbb {R}.\] The theory established shows the existence of global solutions in Sobolev spaces with order below the one given by the energy space $H^1(\mathbb {R})$, i.e. solutions corresponding to data $u_0\in H^s(\mathbb {R})$, $s>3/4$, with $\|u_0\|_{L^2}<\|Q\|_{L^2}$, where $Q$ is the solitary wave solution of the equation.References
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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
- MR Author ID: 343833
- Email: linares@impa.br
- G. Ponce
- Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
- MR Author ID: 204988
- Email: ponce@math.ucsb.edu
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 1847-1855
- MSC (2000): Primary 35Q53
- DOI: https://doi.org/10.1090/S0002-9939-02-06871-5
- MathSciNet review: 1955273