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The wave maps equation and Brownian paths
Bjoern Bringmann, Jonas Luhrmann, Gigliola Staffilani · 2021-11-15 · via math.PR updates on arXiv.org

We discuss the $(1+1)$-dimensional wave maps equation with values in a compact Riemannian manifold $\mathcal{M}$. Motivated by the Gibbs measure problem, we consider Brownian paths on the manifold $\mathcal{M}$ as initial data. Our main theorem is the probabilistic local well-posedness of the associated initial value problem. The analysis in this setting combines analytic, geometric, and probabilistic methods.

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