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arXiv · 1902.01125

Inhomogeneous Strichartz estimates in some critical cases

Neal Bez·Jayson Cunanan·Sanghyuk Lee
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Abstract

Strong-type inhomogeneous Strichartz estimates are shown to be false for the wave equation outside the so-called acceptable region. On a critical line where the acceptability condition marginally fails, we prove substitute estimates with a weak-type norm in the temporal variable. We achieve this by establishing such weak-type inhomogeneous Strichartz estimates in an abstract setting. The application to the wave equation rests on a slightly stronger form of the standard dispersive estimate in terms of certain Besov spaces.

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Neal Bez, Jayson Cunanan, Sanghyuk Lee. 2019-02-04. Inhomogeneous Strichartz estimates in some critical cases. https://arxiv.org/abs/1902.01125

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