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Quadratic forms for the 1-D semilinear Schrödinger equation |
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| Authors: | Carlos E. Kenig Gustavo Ponce Luis Vega |
| Affiliation: | Department of Mathematics, University of Chicago, Chicago, Illinois 60637 ; Department of Mathematics, University of California, Santa Barbara, California 93106 ; Departamento de Matematicas, Universidad del Pais Vasco, Apartado 644, 48080 Bilbao, Spain |
| 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. |
| Keywords: | Schrö dinger equation, bilinear estimates, well-posedness |
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