Quadratic forms for the 1-D semilinear Schrödinger equation
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- by Carlos E. Kenig, Gustavo Ponce and Luis Vega PDF
- Trans. Amer. Math. Soc. 348 (1996), 3323-3353 Request permission
Abstract:
This paper is concerned with 1-D quadratic semilinear Schrödinger equations. We study local well posedness in classical Sobolev space $H^s$ of the associated initial value problem and periodic boundary value problem. Our main interest is to obtain the lowest value of $s$ which guarantees the desired local well posedness result. We prove that at least for the quadratic cases these values are negative and depend on the structure of the nonlinearity considered.References
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Additional Information
- Carlos E. Kenig
- Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
- MR Author ID: 100230
- Email: cek@math.uchicago.edu
- Gustavo Ponce
- Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
- MR Author ID: 204988
- Email: ponce@math.ucsb.edu
- Luis Vega
- Affiliation: Departamento de Matematicas, Universidad del Pais Vasco, Apartado 644, 48080 Bilbao, Spain
- MR Author ID: 237776
- Email: MTPVEGOL@lg.ehu.es
- Received by editor(s): May 17, 1995
- Additional Notes: C. E. Kenig and G. Ponce were supported by NSF grants. L. Vega was supported by a DGICYT grant.
- © Copyright 1996 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 348 (1996), 3323-3353
- MSC (1991): Primary 35K22; Secondary 35P05
- DOI: https://doi.org/10.1090/S0002-9947-96-01645-5
- MathSciNet review: 1357398