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

Abstract 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.