Sharp Strichartz estimates in spherical coordinates
Robert Schippa
Communications on Pure & Applied Analysis 2017, 16(6): 2047-2051 doi: 10.3934/cpaa.2017100

We prove Strichartz estimates found after adding regularity in the spherical coordinates for Schrödinger-like equations. The obtained estimates are sharp up to endpoints. The proof relies on estimates involving spherical averages, which were obtained in [5]. We discuss sharpness making use of a modified Knapp-type example.

keywords: Dispersive equations Strichartz estimates spherical symmetry spherical averages angular regularity
Generalized inhomogeneous Strichartz estimates
Robert Schippa
Discrete & Continuous Dynamical Systems - A 2017, 37(6): 3387-3410 doi: 10.3934/dcds.2017143

We prove new inhomogeneous generalized Strichartz estimates, which do not follow from the homogeneous generalized estimates by virtue of the Christ-Kiselev lemma. Instead, we make use of the bilinear interpolation argument worked out by Keel and Tao and refined by Foschi presented in a unified framework. Finally, we give a sample application.


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