随机Hardy-Littlewood-Sobolev不等式及其在噪声色散的Strichartz估计中的应用

Annales Henri Lebesgue Pub Date : 2022-05-04 DOI:10.5802/ahl.122

Romain Duboscq, Anthony Reveillac

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引用次数: 4

摘要

本文研究了一类随机Hardy-Littlewood-Sobolev不等式。由于不等式中势的非齐次性质，右边出现一个与区间长度成正比的常数。作为直接应用，我们导出了随机调制色散的局部Strichartz估计，并解决了临界非线性Schrödinger方程的Cauchy问题。

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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On a stochastic Hardy–Littlewood–Sobolev inequality with application to Strichartz estimates for a noisy dispersion

In this paper, we investigate a stochastic Hardy-Littlewood-Sobolev inequality. Due to the non-homogenous nature of the potential in the inequality, a constant proportional to the length of the interval appears on the right-hand-side. As a direct application, we derive local Strichartz estimates for randomly modulated dispersions and solve the Cauchy problem of the critical nonlinear Schrödinger equation.

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Annales Henri Lebesgue

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