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<p>We perturb the 3D Euler equations by a particular non-linear Stratonovich noise. We show the existence and uniqueness of a global-in-time (i.e. no blow-up) smooth solution. The result is a corollary of a more general theorem valid in an abstract framework, where the addition of such noise prevents the blow-up possibly induced by a drift with super-linear growth. A similar conclusion applies to a class of SPDEs satisfying a generalized coercivity property, which includes the 3D Navier–Stokes equations. All results obtained are new in the context of Stratonovich noise.</p>

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A suitable nonlinear Stratonovich noise prevents blow-up in the Euler equations and other SPDEs

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月13日

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  • Marco Bagnara

摘要

We perturb the 3D Euler equations by a particular non-linear Stratonovich noise. We show the existence and uniqueness of a global-in-time (i.e. no blow-up) smooth solution. The result is a corollary of a more general theorem valid in an abstract framework, where the addition of such noise prevents the blow-up possibly induced by a drift with super-linear growth. A similar conclusion applies to a class of SPDEs satisfying a generalized coercivity property, which includes the 3D Navier–Stokes equations. All results obtained are new in the context of Stratonovich noise.