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- W2467134150 abstract "The purpose of this paper is to study the validity of global-in-time Strichartz estimates for the Schrodinger equation on $mathbb{R}^n$, $nge3$, with the negative inverse-square potential $-sigma|x|^{-2}$ in the critical case $sigma=(n-2)^2/4$. It turns out that the situation is different from the subcritical case $sigma<(n-2)^2/4$ in which the full range of Strichartz estimates is known to be hold. More precisely, splitting the solution into the radial and non-radial parts, we show that (i) the radial part satisfies a weak-type endpoint estimate, which can be regarded as an extension to higher dimensions of the endpoint Strichartz estimate with radial data for the two-dimensional free Schrodinger equation; (ii) other endpoint estimates in Lorentz spaces for the radial part fail in general; (iii) the non-radial part satisfies the full range of Strichartz estimates." @default.
- W2467134150 created "2016-07-22" @default.
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- W2467134150 date "2016-07-11" @default.
- W2467134150 modified "2023-09-26" @default.
- W2467134150 title "Remarks on endpoint Strichartz estimates for Schrodinger equations with the critical inverse-square potential" @default.
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- W2467134150 doi "https://doi.org/10.48550/arxiv.1607.02848" @default.
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