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.
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This material is based upon work supported by the National Science Foundation under agreement No. DMS-0635607 and The S. S. Chern Fund. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation or The S. S. Chern Fund.
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Guo, Z., Wang, Y. Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations. JAMA 124, 1–38 (2014). https://doi.org/10.1007/s11854-014-0025-6
- Dispersive Equation
- Nonlinear Wave Equation
- Critical Regularity
- Strichartz Estimate
- Radial Case