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Low regularity solutions for a 2D quadratic nonlinear Schrödinger equation
Author(s):
Ioan
Bejenaru;
Daniela
De Silva
Journal:
Trans. Amer. Math. Soc.
360
(2008),
5805-5830.
MSC (2000):
Primary 35Q55
Posted:
June 19, 2008
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Abstract:
We establish that the initial value problem for the quadratic non-linear Schrödinger equation where  , is locally well-posed in  when  . The critical exponent for this problem is  , and previous work by Colliander, Delort, Kenig and Staffilani, 2001, established local well-posedness for  .
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Additional Information:
Ioan
Bejenaru
Affiliation:
Department of Mathematics, University of California, Los Angeles, California 90095
Address at time of publication:
Department of Mathematics, Texas A & M University, College Station, Texas 77843
Daniela
De Silva
Affiliation:
Department of Mathematics, Johns Hopkins University, 3400 N. Charles Street, Baltimore, Maryland 21218
Address at time of publication:
Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
DOI:
10.1090/S0002-9947-08-04415-2
PII:
S 0002-9947(08)04415-2
Received by editor(s):
August 21, 2006
Posted:
June 19, 2008
Additional Notes:
The authors were partially supported by the Mathematical Sciences Research Institute (MSRI) at Berkeley.
Copyright of article:
Copyright
2008,
American Mathematical Society
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