Pathwise uniqueness by noise for singular stochastic PDEs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915686561873920 |
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| author | Addona, Davide Bignamini, Davide Orrieri, Carlo Scarpa, Luca |
| author_facet | Addona, Davide Bignamini, Davide Orrieri, Carlo Scarpa, Luca |
| contents | Pathwise uniqueness for stochastic PDEs with drift in differential form is a main open problem in the recent literature on regularisation by noise. This paper establishes a self-contained theory in the framework of stochastic evolution equations on separable Hilbert spaces and provides a first result to address such an issue. The singularity of the drift allows to achieve novel uniqueness results for several classes of examples, ranging from fluid-dynamics to phase-separation models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17736 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pathwise uniqueness by noise for singular stochastic PDEs Addona, Davide Bignamini, Davide Orrieri, Carlo Scarpa, Luca Probability Analysis of PDEs 60H15, 35R60, 35R15 Pathwise uniqueness for stochastic PDEs with drift in differential form is a main open problem in the recent literature on regularisation by noise. This paper establishes a self-contained theory in the framework of stochastic evolution equations on separable Hilbert spaces and provides a first result to address such an issue. The singularity of the drift allows to achieve novel uniqueness results for several classes of examples, ranging from fluid-dynamics to phase-separation models. |
| title | Pathwise uniqueness by noise for singular stochastic PDEs |
| topic | Probability Analysis of PDEs 60H15, 35R60, 35R15 |
| url | https://arxiv.org/abs/2512.17736 |