Invariant measures for mKdV and KdV in infinite volume
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911751409238016 |
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| author | Forlano, Justin Killip, Rowan Visan, Monica |
| author_facet | Forlano, Justin Killip, Rowan Visan, Monica |
| contents | We construct dynamics for the defocusing real-valued (Miura) mKdV equation on the real line with initial data distributed according to Gibbs measure. We also prove that Gibbs measure is invariant under these dynamics. On the way, we provide a new proof of the invariance of the Gibbs measure under mKdV on the torus.
Building on these results, we construct new measure-preserving dynamics for the KdV equation on the whole real line. Samples from this family of measures exhibit the same local regularity as white-noise, but completely different statistics! |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04292 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Invariant measures for mKdV and KdV in infinite volume Forlano, Justin Killip, Rowan Visan, Monica Analysis of PDEs We construct dynamics for the defocusing real-valued (Miura) mKdV equation on the real line with initial data distributed according to Gibbs measure. We also prove that Gibbs measure is invariant under these dynamics. On the way, we provide a new proof of the invariance of the Gibbs measure under mKdV on the torus. Building on these results, we construct new measure-preserving dynamics for the KdV equation on the whole real line. Samples from this family of measures exhibit the same local regularity as white-noise, but completely different statistics! |
| title | Invariant measures for mKdV and KdV in infinite volume |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.04292 |