Finite speed of propagation for the 2- and 3-dimensional multiplicative stochastic wave equation

TL;DR

This paper establishes finite speed of propagation for the 2D and 3D multiplicative stochastic wave equations, enabling global well-posedness results for the cubic nonlinear case in the energy space.

Contribution

It proves finite speed of propagation for stochastic wave equations in higher dimensions, a key step towards global solutions for nonlinear stochastic wave equations.

Findings

Finite speed of propagation is established in 2D and 3D.

Global well-posedness is achieved for the cubic nonlinear stochastic wave equation.

Results extend understanding of stochastic wave dynamics in higher dimensions.

Abstract

We prove finite speed of propagation for the multiplicative stochastic wave equation in two and three dimensions which leads us to a global space-time well-posedness result for the cubic nonlinear equation in the analogue of the energy space.