Stochastic Convective Wave Equation in Two Space Dimension

Abstract

We study the convective wave equation in two space dimension driven by spatially homogeneous Gaussian noise. The existence of the real-valued solution is proved by providing a necessary and sufficient condition of Gaussian noise source. Our approach is based on the mild solution of the convective wave equation which is constructed by Walsh's theory of martingale measures. H\"older continuity of the solution is proved by using Green's function and Kolmogorov continuity theorem.