A stochastic wave equation in two space dimension: Smoothness of the law

We prove the existence and uniqueness, for any time, of a real-valued proce ss solving a nonlinear stochastic wave equation driven by a Gaussian noise white in time and correlated in the two-dimensional space variable. We prov e that the solution is regular in the sense of the Malliavin calculus. We a lso give a decay condition on the covariance function of the noise under wh ich the solution has Holder continuous trajectories and show that, under an additional ellipticity assumption, the law of the solution at any strictly positive time has a smooth density.