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arXiv · 2603.05050

Regularization by noise for Gevrey well-posedeness of a weakly hyperbolic operator

Enrico Bernardi·Alberto Lanconelli
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Abstract

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 $ .

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Enrico Bernardi, Alberto Lanconelli. 2026-03-05. Regularization by noise for Gevrey well-posedeness of a weakly hyperbolic operator. https://arxiv.org/abs/2603.05050

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