  In this article, we study the stochastic wave equation on the entire space
$\mathbb{R}^d$, driven by a space-time L\'evy white noise with possibly
infinite variance (such as the $\alpha$-stable L\'evy noise). In this equation,
the noise is multiplied by a Lipschitz function $\sigma(u)$ of the solution. We
assume that the spatial dimension is $d=1$ or $d=2$. Under general conditions
on the L\'evy measure of the noise, we prove the existence of the solution, and
we show that, as a function-valued process, the solution has a c\`adl\`ag
modification in the local fractional Sobolev space of order $r<1/4$ if $d=1$,
respectively $r<-1$ if $d=2$.
