洛伦兹型空间中的正规斯特里查兹估计值与对 $H^s$ 临界非均质双谐波 NLS 方程的应用

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-10 DOI:arxiv-2409.06278

RoeSong Jang, JinMyong An, JinMyong Kim

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摘要

本文研究了$H^s$临界同调双谐非线性薛定谔方程（IBNLS）的考奇问题（[iu_{t}\pm\Delta^{2} u=\lambda |x|^{-b}|u|^{sigma}u,~u(0)=u_{0}\in H^{s} (\mathbbR^{d}),\] 其中 $\lambda\in \mathbb C$, $d\ge 3$, $1\le s本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Regular Strichartz estimates in Lorentz-type spaces with application to the $H^s$-critical inhomogeneous biharmonic NLS equation

In this paper, we investigate the Cauchy problem for the $H^s$-critical inhomogeneous biharmonic nonlinear Schr\"{o}dinger (IBNLS) equation \[iu_{t}\pm \Delta^{2} u=\lambda |x|^{-b}|u|^{\sigma}u,~u(0)=u_{0} \in H^{s} (\mathbb R^{d}),\] where $\lambda\in \mathbb C$, $d\ge 3$, $1\le s<\frac{d}{2}$, $0

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arXiv - MATH - Analysis of PDEs

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