On a stochastic Hardy–Littlewood–Sobolev inequality with application to Strichartz estimates for a noisy dispersion
Annales Henri Lebesgue, Volume 5 (2022), pp. 263-274.

Metadata

KeywordsStochastic regularization, Stochastic Partial Differential Equations, Nonlinear Schrödinger equation, Hardy–Littlewood–Sobolev inequality

Abstract

In this paper, we investigate a stochastic Hardy–Littlewood–Sobolev inequality. Due to the non-homogenous nature of the potential in the inequality, we show that 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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