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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.31359 |
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| _version_ | 1866917548097798144 |
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| author | Merino, Pablo |
| author_facet | Merino, Pablo |
| contents | We provide a complementary result to the quasi-invariance of Gaussian measures supported on Sobolev spaces with high regularity under the dynamics of the three-dimensional periodic defocusing nonlinear wave equation from Gunaratnam-Oh-Tzvetkov-Weber (2022). Namely, given $p$ and $σ$ large enough, we prove the existence of dense sets of Sobolev spaces $W^{σ,p}(\mathbb{T}^3)$ which do not preserve the regularity $σ$ throughout the aforementioned dynamics. This is in sharp contrast with the propagation under the flow of almost sure properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_31359 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A pathological set regarding the propagation of almost sure properties of Gaussian measures Merino, Pablo Analysis of PDEs 35L05, 35R60 We provide a complementary result to the quasi-invariance of Gaussian measures supported on Sobolev spaces with high regularity under the dynamics of the three-dimensional periodic defocusing nonlinear wave equation from Gunaratnam-Oh-Tzvetkov-Weber (2022). Namely, given $p$ and $σ$ large enough, we prove the existence of dense sets of Sobolev spaces $W^{σ,p}(\mathbb{T}^3)$ which do not preserve the regularity $σ$ throughout the aforementioned dynamics. This is in sharp contrast with the propagation under the flow of almost sure properties. |
| title | A pathological set regarding the propagation of almost sure properties of Gaussian measures |
| topic | Analysis of PDEs 35L05, 35R60 |
| url | https://arxiv.org/abs/2605.31359 |