Mathematics

Inspired by problems from fluid dynamics, we introduce an approach to obtain lower bounds for Lyapunov exponents of stochastic PDEs. Our proof relies on the introduction of a novel Lyapunov functional for the projective process associated to the equation, based on the study of dynamics of the energy median and on a notion of non-degeneracy of the noise that leads to high-frequency stochastic instability. Joint work with M. Hairer, and in progress with M. Hairer, S. Punshon-Smith and J. Yi.