Strichartz estimates for the Schrödinger equation with radial data
Author:
Atanas Stefanov
Journal:
Proc. Amer. Math. Soc. 129 (2001), 13951401
MSC (1991):
Primary 35J10; Secondary 42B15
Published electronically:
October 25, 2000
MathSciNet review:
1814165
Fulltext PDF Free Access
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References 
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Abstract: We prove an endpoint Strichartz estimate for radial solutions of the twodimensional Schrödinger equation:
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 J. Ginibre and G. Velo, Smoothing Properties and Retarded estimates for Some Dispersive Evolution Equations, Comm. Math. Phys. 123 (1989), 535573.
 2.
 M. Keel and T. Tao, Endpoint Strichartz Estimates, Amer. J. Math. 120 (1998), 955980. CMP 99:01
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 S. Klainerman and M. Machedon, Spacetime estimates for null forms and the local existence theorem, Comm. Pure Appl. Math. 46 (1993), 12211268. MR 94h:35137
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 G. Mockenhaupt, A. Seeger, C.D. Sogge, Local Smoothing of Fourier Integrals and CarlesonSjölin Estimates, J. Amer. Math. Soc. 6 (1993), 65130. MR 93h:58150
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 S.J. MontgomerySmith, Time Decay for the Bounded Mean Oscillation of Solutions of the Schrödinger and Wave Equations, Duke Math. J. 91 (1998), no. 2, 393408. MR 99e:35006
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 D. Müller, A. Seeger, Inequalities for Spherically Symmetric Solutions of the Wave Equation, Math. Z. 218 (1995), 417426. MR 96e:35093
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 R.S. Strichartz, Restriction of Fourier Transform to Quadratic Surfaces and Decay of Solutions of Wave Equations, Duke Math. J. 44, (1977), 705714. MR 58:23577
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 T. Tao, Counterexamples to the Endpoint Strichartz estimate for the wave equation, (1998), preprint.
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 M.C. Vilela, Regularity for the solutions to the free Schrödinger equation with radial initial data, preprint.
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 K. Yajima, Existence of solutions for Schrödinger evolution equations, Comm. Math. Phys. 110 (1987), 415426. MR 88e:35048
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Additional Information
Atanas Stefanov
Affiliation:
Department of Mathematics, Syracuse University, Syracuse, New York 13244
Email:
astefano@syr.edu
DOI:
http://dx.doi.org/10.1090/S0002993900057221
PII:
S 00029939(00)057221
Keywords:
Schr\"odinger equation,
Strichartz estimates
Received by editor(s):
August 6, 1999
Published electronically:
October 25, 2000
Additional Notes:
This research was supported in part by DMS9870027
Communicated by:
Christopher D. Sogge
Article copyright:
© Copyright 2000
American Mathematical Society
