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arXiv · 2111.07381

The wave maps equation and Brownian paths

Bjoern Bringmann·Jonas Luhrmann·Gigliola Staffilani
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Abstract

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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Bjoern Bringmann, Jonas Luhrmann, Gigliola Staffilani. 2021-11-14. The wave maps equation and Brownian paths. https://arxiv.org/abs/2111.07381

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