The wave maps equation and Brownian paths
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866912404360658944 |
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| author | Bringmann, Bjoern Luhrmann, Jonas Staffilani, Gigliola |
| author_facet | Bringmann, Bjoern Luhrmann, Jonas Staffilani, Gigliola |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_07381 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The wave maps equation and Brownian paths Bringmann, Bjoern Luhrmann, Jonas Staffilani, Gigliola Analysis of PDEs Mathematical Physics Probability 35L05, 53E99, 60L40 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. |
| title | The wave maps equation and Brownian paths |
| topic | Analysis of PDEs Mathematical Physics Probability 35L05, 53E99, 60L40 |
| url | https://arxiv.org/abs/2111.07381 |