Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations

We prove some new Strichartz estimates for a class of dispersive equations with radial initial data. In particular, we obtain the full radial Strichartz estimates up to some endpoints for the Schrödinger equation. Using these estimates, we obtain some new results related to nonlinear problems, inclu...

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Bibliographic Details
Published in:Journal d'analyse mathématique (Jerusalem) 2014-10, Vol.124 (1), p.1-38
Main Authors: Guo, Zihua, Wang, Yuzhao
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Analysis
Dynamical Systems and Ergodic Theory
Estimates
Functional Analysis
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinearity
Partial Differential Equations
Scattering
Schroedinger equation
Wave equations
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Summary:We prove some new Strichartz estimates for a class of dispersive equations with radial initial data. In particular, we obtain the full radial Strichartz estimates up to some endpoints for the Schrödinger equation. Using these estimates, we obtain some new results related to nonlinear problems, including small data scattering and large data LWP for the nonlinear Schrödinger and wave equations with radial critical initial data and the well-posedness theory for the fractional order Schrödinger equation in the radial case.
ISSN:0021-7670
1565-8538
DOI:10.1007/s11854-014-0025-6