Abstract
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.
Original language | English |
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Pages (from-to) | 1–38 |
Journal | Journal d'Analyse Mathématique |
Volume | 124 |
Issue number | 1 |
DOIs | |
Publication status | Published - Oct 2014 |
Keywords
- Dispersive Equation
- Nonlinear Wave Equation
- Critical Regularity
- Strichartz Estimate
- Radial Case