Invariant Gibbs dynamics for two-dimensional fractional wave equations in negative Sobolev spaces
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866918165824405504 |
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| author | Forcella, Luigi Pocovnicu, Oana |
| author_facet | Forcella, Luigi Pocovnicu, Oana |
| contents | We consider a fractional nonlinear wave equations (fNLW) with a general power-type nonlinearity, on the two-dimensional torus. Our main goal is to construct invariant global-in-time Gibbs dynamics for a renormalized fNLW. We first construct the Gibbs measure associated with this equation by using the variational approach of Barashkov and Gubinelli. We then prove almost sure local well-posedness with respect to Gibbsian initial data, by exploiting the second order expansion. Finally, we extend solutions globally in time using Bourgain's invariant measure argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_07857 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Invariant Gibbs dynamics for two-dimensional fractional wave equations in negative Sobolev spaces Forcella, Luigi Pocovnicu, Oana Analysis of PDEs Probability We consider a fractional nonlinear wave equations (fNLW) with a general power-type nonlinearity, on the two-dimensional torus. Our main goal is to construct invariant global-in-time Gibbs dynamics for a renormalized fNLW. We first construct the Gibbs measure associated with this equation by using the variational approach of Barashkov and Gubinelli. We then prove almost sure local well-posedness with respect to Gibbsian initial data, by exploiting the second order expansion. Finally, we extend solutions globally in time using Bourgain's invariant measure argument. |
| title | Invariant Gibbs dynamics for two-dimensional fractional wave equations in negative Sobolev spaces |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2306.07857 |