Intermittency for the wave equation with L\'evy white noise

TL;DR

This paper studies the stochastic wave equation driven by Le9vy white noise, establishing a maximal inequality for moments and demonstrating the solution's weak intermittency in one dimension.

Contribution

It introduces a maximal inequality for moments of the integral with respect to Le9vy white noise and proves the weak intermittency of the solution.

Findings

Established a maximal inequality for moments of the noise integral.

Proved the existence and uniqueness of the solution.

Demonstrated the solution's weak intermittency property.

Abstract

In this article, we consider the stochastic wave equation in dimension 1 driven by the L\'evy white noise introduced in Balan (2015). Using Rosenthal's inequality, we develop a maximal inequality for the moments of order $p \geq 2$ of the integral with respect to this noise. Based on this inequality, we show that this equation has a unique solution, which is weakly intermittent in the sense of Foondun and Khoshnevisan (2009) and Khoshnevisan (2014).