Regularization by noise for Gevrey well-posedeness of a weakly hyperbolic operator
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911488488243200 |
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| author | Bernardi, Enrico Lanconelli, Alberto |
| author_facet | Bernardi, Enrico Lanconelli, Alberto |
| contents | We present an example of a linear partial differential equation whose Cauchy problem becomes well-posed when perturbed by noise. Specifically, we make clear how a suitable multiplicative Stratonovich perturbation of Brownian type renders a weakly hyperbolic operator with double involutive characteristics well-posed in the $C^{\infty}$-category, while its deterministic counterpart is only well-posed in the Gevrey $ s $ classes with $ 1 \leq s <2 $ . |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05050 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Regularization by noise for Gevrey well-posedeness of a weakly hyperbolic operator Bernardi, Enrico Lanconelli, Alberto Probability Analysis of PDEs 60H15, 35L10, 60H50 We present an example of a linear partial differential equation whose Cauchy problem becomes well-posed when perturbed by noise. Specifically, we make clear how a suitable multiplicative Stratonovich perturbation of Brownian type renders a weakly hyperbolic operator with double involutive characteristics well-posed in the $C^{\infty}$-category, while its deterministic counterpart is only well-posed in the Gevrey $ s $ classes with $ 1 \leq s <2 $ . |
| title | Regularization by noise for Gevrey well-posedeness of a weakly hyperbolic operator |
| topic | Probability Analysis of PDEs 60H15, 35L10, 60H50 |
| url | https://arxiv.org/abs/2603.05050 |