Strichartz estimates for the Schrödinger equation with radial data

Author:
Atanas Stefanov

Journal:
Proc. Amer. Math. Soc. **129** (2001), 1395-1401

MSC (1991):
Primary 35J10; Secondary 42B15

DOI:
https://doi.org/10.1090/S0002-9939-00-05722-1

Published electronically:
October 25, 2000

MathSciNet review:
1814165

Full-text PDF

Abstract | References | Similar Articles | Additional Information

We prove an endpoint Strichartz estimate for *radial* solutions of the two-dimensional Schrödinger equation:

**1.**J. Ginibre and G. Velo,*Smoothing Properties and Retarded estimates for Some Dispersive Evolution Equations*, Comm. Math. Phys.**123**(1989), 535-573.**2.**M. Keel and T. Tao,*Endpoint Strichartz Estimates*, Amer. J. Math.**120**(1998), 955-980. CMP**99:01****3.**S. Klainerman and M. Machedon,*Space-time estimates for null forms and the local existence theorem*, Comm. Pure Appl. Math.**46**(1993), 1221-1268. MR**94h:35137****4.**G. Mockenhaupt, A. Seeger, C.D. Sogge,*Local Smoothing of Fourier Integrals and Carleson-Sjölin Estimates*, J. Amer. Math. Soc.**6**(1993), 65-130. MR**93h:58150****5.**S.J. Montgomery-Smith,*Time Decay for the Bounded Mean Oscillation of Solutions of the Schrödinger and Wave Equations*, Duke Math. J.**91**(1998), no. 2, 393-408. MR**99e:35006****6.**D. Müller, A. Seeger,*Inequalities for Spherically Symmetric Solutions of the Wave Equation*, Math. Z.**218**(1995), 417-426. MR**96e:35093****7.**R.S. Strichartz,*Restriction of Fourier Transform to Quadratic Surfaces and Decay of Solutions of Wave Equations*, Duke Math. J.**44**, (1977), 705-714. MR**58:23577****8.**E. M. Stein,*Harmonic analysis: Real variable methods, orthogonality, and oscillatory integrals*, Princeton University Press, Princeton NJ, 1993. MR**95c:42002****9.**T. Tao,*Counterexamples to the Endpoint Strichartz estimate for the wave equation*, (1998), preprint.**10.**M.C. Vilela,*Regularity for the solutions to the free Schrödinger equation with radial initial data*, preprint.**11.**K. Yajima,*Existence of solutions for Schrödinger evolution equations*, Comm. Math. Phys.**110**(1987), 415-426. 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:
https://doi.org/10.1090/S0002-9939-00-05722-1

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 DMS-9870027

Communicated by:
Christopher D. Sogge

Article copyright:
© Copyright 2000
American Mathematical Society