Quadratic forms for the 1-D semilinear Schrödinger equation

Authors:
Carlos E. Kenig, Gustavo Ponce and Luis Vega

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

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with 1-D quadratic semilinear

Schrödinger equations. We study local well posedness in classical Sobolev space of the associated initial value problem and periodic boundary value problem. Our main interest is to obtain the lowest value of 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.

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Additional Information

**Carlos E. Kenig**

Affiliation:
Department of Mathematics, University of Chicago, Chicago, Illinois 60637

Email:
cek@math.uchicago.edu

**Gustavo Ponce**

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

Email:
ponce@math.ucsb.edu

**Luis Vega**

Affiliation:
Departamento de Matematicas, Universidad del Pais Vasco, Apartado 644, 48080 Bilbao, Spain

Email:
MTPVEGOL@lg.ehu.es

DOI:
https://doi.org/10.1090/S0002-9947-96-01645-5

Keywords:
Schrödinger equation,
bilinear estimates,
well-posedness

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.

Article copyright:
© Copyright 1996
American Mathematical Society