Sharp weighted Strichartz estimates and critical inhomogeneous Hartree equations

Seongyeon Kim; Yoonjung Lee; Ihyeok Seo

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arXiv · 2110.14922

Sharp weighted Strichartz estimates and critical inhomogeneous Hartree equations

Seongyeon Kim·Yoonjung Lee·Ihyeok Seo

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Abstract

We study the Cauchy problem for the inhomogeneous Hartree equation in this paper. Although its well-posedness theory has been extensively studied in recent years, much less is known compared to the classical Hartree model of homogeneous type. In particular, the problem of Sobolev initial data with the Sobolev critical index remains unsolved. The main contribution of this paper is to establish the local existence of solutions to the inhomogeneous equation in the critical cases. To do so, we obtain all possible $L^p$ Strichartz estimates with singular weights.

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Seongyeon Kim, Yoonjung Lee, Ihyeok Seo. 2021-10-28. Sharp weighted Strichartz estimates and critical inhomogeneous Hartree equations. https://arxiv.org/abs/2110.14922

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