## Bilinear estimates and applications to 2d NLS

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- by J. E. Colliander, J.-M. Delort, C. E. Kenig and G. Staffilani PDF
- Trans. Amer. Math. Soc.
**353**(2001), 3307-3325 Request permission

## Abstract:

The three bilinearities $u v, \overline {uv},\overline {u}v$ for functions $u, v : \mathbb {R}^2 \times [0,T] \longmapsto \mathbb {C}$ are sharply estimated in function spaces $X_{s,b}$ associated to the Schrödinger operator $i \partial _t + \Delta$. These bilinear estimates imply local wellposedness results for Schrödinger equations with quadratic nonlinearity. Improved bounds on the growth of spatial Sobolev norms of finite energy global-in-time and blow-up solutions of the cubic nonlinear Schrödinger equation (and certain generalizations) are also obtained.## References

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## Additional Information

**J. E. Colliander**- Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
- Email: colliand@math.berkeley.edu
**J.-M. Delort**- Affiliation: Département of Mathématiques, Université de Paris-Nord, 93430 Villetaneuse, France
- Email: delort@math.univ-paris13.fr
**C. E. Kenig**- Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
- MR Author ID: 100230
- Email: cek@math.uchicago.edu
**G. Staffilani**- Affiliation: Department of Mathematics, Stanford University, Stanford California 94305
- MR Author ID: 614986
- Email: gigliola@math.stanford.edu
- Received by editor(s): July 24, 2000
- Published electronically: April 10, 2001
- Additional Notes: J.E.C. was supported in part by an N.S.F. Postdoctoral Research Fellowship.

C.E.K. was supported in part by N.S.F. Grant DMS 9500725

G.S. was supported in part by N.S.F. Grant DMS 9800879 - © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**353**(2001), 3307-3325 - MSC (2000): Primary 35Q55, 42B35
- DOI: https://doi.org/10.1090/S0002-9947-01-02760-X
- MathSciNet review: 1828607