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We give the necessary and sufficient condition for the solvability of thestochastic wave equation $ \frac{\partial^2 }{\partial t^2}u(t,x) =\Deltau(t,x)+\dot{W}(t,x)$ on $\mathbb{R}^d$, where $W(t,x)$ is a fractional Brownianfield with temporal Hurst parameter $H_0>1/2$ and spatial Hurst parameters$H_i\in(0,1)$ for $i=1,\cdots,d$. Moreover, we obtain the growth rate and theH\"older continuity of the solution on the whole space $\mathbb{R}^d$ when$d=1$ and $H_0=1/2$.

Stochastic wave equation with additive fractional noise: solvability and global H\"older continuity