No blow-up by nonlinear It\^o noise for the Euler equations
Probability
2025-05-30 v2
Abstract
By employing a suitable multiplicative It\^o noise with radial structure and with more than linear growth, we show the existence of a unique, global-in-time, strong solution for the stochastic Euler equations in two and three dimensions. More generally, we consider a class of stochastic partial differential equations (SPDEs) with a superlinear growth drift and suitable nonlinear, multiplicative It\^o noise, with the stochastic Euler equations as a special case within this class. We prove that the addition of such a noise effectively prevents blow-ups in the solution of these SPDEs.
Keywords
Cite
@article{arxiv.2305.09852,
title = {No blow-up by nonlinear It\^o noise for the Euler equations},
author = {Marco Bagnara and Mario Maurelli and Fanhui Xu},
journal= {arXiv preprint arXiv:2305.09852},
year = {2025}
}
Comments
Revised version accepted in Electron. J. Probab