Dissipative solutions to randomly forced 3D Euler equations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908867704651776 |
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| author | Pappalettera, Umberto Triggiano, Francesco |
| author_facet | Pappalettera, Umberto Triggiano, Francesco |
| contents | The purpose of this work is twofold. First, we construct probabilistically strong solutions to the three-dimensional Euler equations perturbed by additive noise that are $\mathbb{P}$-almost surely continuous in time, Hölder in space, and satisfy the local energy inequality up to an arbitrarily large stopping time. Second, we prove several non-unique ergodicity results for the forced Euler equations with continuous-in-time external forcing. The solutions we construct are genuinely random and, almost surely, strictly dissipative and not steady states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21616 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dissipative solutions to randomly forced 3D Euler equations Pappalettera, Umberto Triggiano, Francesco Analysis of PDEs Probability The purpose of this work is twofold. First, we construct probabilistically strong solutions to the three-dimensional Euler equations perturbed by additive noise that are $\mathbb{P}$-almost surely continuous in time, Hölder in space, and satisfy the local energy inequality up to an arbitrarily large stopping time. Second, we prove several non-unique ergodicity results for the forced Euler equations with continuous-in-time external forcing. The solutions we construct are genuinely random and, almost surely, strictly dissipative and not steady states. |
| title | Dissipative solutions to randomly forced 3D Euler equations |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2511.21616 |