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arXiv · 1601.07643

Inhomogeneous Strichartz estimates for Schrödinger's equation

Youngwoo Koh·Ihyeok Seo
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Abstract

Foschi and Vilela in their independent works (\cite{F},\cite{V}) showed that the range of $(1/r,1/\widetilde{r})$ for which the inhomogeneous Strichartz estimate $ \big\|\int_{0}^{t}e^{i(t-s)Δ}F(\cdot,s)ds\big\|_{L^{q}_tL^{r}_x} \lesssim \|F\|_{L^{\widetilde{q}'}_tL^{\widetilde{r}'}_x} $ holds for some $q,\widetilde{q}$ is contained in the closed pentagon with vertices $A,B,B',P,P'$ except the points $P,P'$ (see Figure 1). We obtain the estimate for the corner points $P,P'$.

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Youngwoo Koh, Ihyeok Seo. 2016-04-23. Inhomogeneous Strichartz estimates for Schrödinger's equation. https://arxiv.org/abs/1601.07643

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