Intermittency for the wave equation with Lévy white noise

Abstract

In this article, we consider the stochastic wave equation in dimension 1 driven by the Lévy white noise introduced in Balan (2015). Using Rosenthal's inequality, we develop a maximal inequality for the moments of order $p\ge 2$ 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).

13 pages