No blow-up by nonlinear It\^o noise for the Euler equations.

We consider the incompressible Euler equations in two or three dimensions and we show that the addition of a suitable multiplicative It\^o noise with superlinear growth prevents a smooth solution from blowing up in finite time. The result is valid for a more general hyperbolic-type SPDE. The proof is based on the Lyapunov function method.
Joint work with Marco Bagnara and Fanhui Xu.