6 papers · 1 filter
Asymptotics of Lyapunov Exponents and Phase Transitions for Fluids with Degenerate Forcing
Martin Hairer, Declan Stacy
In this paper we analyze the Lyapunov exponents of a slow-fast system where the slow component is an Ornstein-Uhlenbeck process which perturbs the linear evolution of a fast variab…
Quasi-Gaussianity of the 2D stochastic Navier-Stokes equations
James Coe, Martin Hairer, Leonardo Tolomeo
We study the qualitative properties of solutions to the 2D stochastic Navier-Stokes equations with forcing that is white in time and coloured in space. Our main result shows that t…
Ergodicity of 2D singular stochastic Navier-Stokes equations
Martin Hairer, Wenhao Zhao
We consider the 2D stochastic Navier-Stokes equations driven by noise that has the regularity of space-time white noise but doesn't exactly coincide with it. We show that, provided…
Ergodicity of infinite volume at high temperature
PaweÅ Duch, Martin Hairer, Jaeyun Yi +1
We consider the infinite volume dynamic and show that it is globally well-posed in a suitable weighted Besov space of distributions. At high temperatures / small coupling,…
A simple construction of the sine-Gordon model via stochastic quantization
Massimiliano Gubinelli, Martin Hairer, Tadahiro Oh +1
We present a simple PDE construction of the sine-Gordon measure below the first threshold ($\be^2 < 4Ï$), in both the finite and infinite volume settings, by studying the correspo…
Lower bounds on the top Lyapunov exponent for linear PDEs driven by the 2D stochastic Navier-Stokes equations
Martin Hairer, Sam Punshon-Smith, Tommaso Rosati +1
We consider the top Lyapunov exponent associated to the advection-diffusion and linearised Navier-Stokes equations on the two-dimensional torus. The velocity field is given by the…