A large deviation principle for nonlinear stochastic wave equation driven by rough noise

This paper is devoted to investigating Freidlin-Wentzell’s large deviation principle for one (spatial) dimensional nonlinear stochastic wave equation $\frac{{\mathrm{\partial }}^2{u}^{\text{e}}(t,x)}{\mathrm{\partial }{t}^2}=\frac{{\mathrm{\partial }}^2{u}^{\text{e}}(t,x)}{\mathrm{\partial }{x}^2}+\sqrt{\text{e}}\sigma (t,x,u^{\text{e}}(t,x))\dot{W}(t,x)$, where $\dot{W}$ is white in time and fractional in space with Hurst parameter $H\in (\frac{1}{4},\frac{1}{2})$. The variational framework and the modified weak convergence criterion proposed by Matoussi et al. \cite{MSZ} are adopted here.