Stochastic geometric wave equations with values in compact Riemannian homogeneous spaces

2011/01/25 by Brzeźniak, Zdzisław, Ondreját, Martin · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1101.4835

Abstract

Let M be a compact Riemannian homogeneous space (e.g. a Euclidean sphere). We prove existence of a global weak solution of the stochastic wave equation \mathbf D_t∂_tu=∑_k=1^d\mathbf D_xk∂_xku+f_u(Du)+g_u(Du) W in any dimension d≥ 1, where f and g are continuous multilinear mappings and W is a spatially homogeneous Wiener process on \mathbb R^d with finite spectral measure. A nonstandard method of constructing weak solutions of SPDEs, that does not rely on martingale representation theorem, is employed.

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