Fractional stochastic wave equation driven by a Gaussian noise rough in space

In this article, we consider fractional stochastic wave equations on R driven by a multiplicative Gaussian noise which is white/colored in time and has the covariance of a fractional Brownian motion with Hurst parameter H ∈ (1/4, 1/2) in space. We prove the existence and uniqueness of the mild Skorohod solution, establish lower and upper bounds for the pth moment of the solution for all p ≥ 2, and obtain the Hölder continuity in time and space variables for the solution.