English

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

Probability 2024-04-16 v2

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. The result is new with Stratonovich noise.

Keywords

Cite

@article{arxiv.2312.10446,
  title  = {A suitable nonlinear Stratonovich noise prevents blow-up in the Euler equations and other SPDEs},
  author = {Marco Bagnara},
  journal= {arXiv preprint arXiv:2312.10446},
  year   = {2024}
}

Comments

Improved result; corrected typos