Hyperbolic Anderson model 2: Strichartz estimates and Stratonovich setting

TL;DR

This paper investigates a wave equation in one and two dimensions with multiplicative Gaussian noise, establishing existence, uniqueness, and Strichartz estimates for solutions in a Stratonovich setting.

Contribution

It develops Strichartz estimates for the wave kernel in weighted Besov spaces, enabling well-posedness results for the stochastic wave equation with Gaussian noise.

Findings

Existence and uniqueness of Stratonovich solutions under certain noise conditions

Development of Strichartz estimates in weighted Besov spaces

Proof of well-posedness for the stochastic wave equation

Abstract

We study a wave equation in dimension $d\in \{1,2\}$ with a multiplicative space-time Gaussian noise. The existence and uniqueness of the Stratonovich solution is obtained under some conditions imposed on the Gaussian noise. The strategy is to develop some Strichartz type estimates for the wave kernel in weighted Besov spaces, by which we can prove the wellposedness of an associated Young-type equation. Those Strichartz bounds are of independent interest.