45 citations · 116 across the 16 of their papers we have counts for
16 papers
Unique ergodicity of projective cocycles over the 2D stochastic Navier-Stokes equations
Sam Punshon-Smith, Tommaso Rosati
We consider the linear cocycles generated by the linearized vorticity equation and by passive scalar advection diffusion, both driven by the two dimensional stochastic Navier-Stoke…
Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds
Jacob Bedrossian, Alex Blumenthal, Sam Punshon-Smith
We develop a general framework for establishing non-uniqueness of stationary measures for stochastically forced dynamical systems possessing an almost surely invariant submanifold.…
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…
Negative regularity mixing for random volume preserving diffeomorphisms
Jacob Bedrossian, Patrick Flynn, Sam Punshon-Smith
We consider the negative regularity mixing properties of random volume preserving diffeomorphisms on a compact manifold without boundary. We give general criteria so that the assoc…
On the norm equivalence of Lyapunov exponents for regularizing linear evolution equations
Alex Blumenthal, Sam Punshon-Smith
We consider the top Lyapunov exponent associated to a dissipative linear evolution equation posed on a separable Hilbert or Banach space. In many applications in partial differenti…
Lower bounds on the Lyapunov exponents of stochastic differential equations
Jacob Bedrossian, Alex Blumenthal, Sam Punshon-Smith
In this article, we review our recently introduced methods for obtaining strictly positive lower bounds on the top Lyapunov exponent of high-dimensional, stochastic differential eq…
Chaos in stochastic 2d Galerkin-Navier-Stokes
Jacob Bedrossian, Sam Punshon-Smith
We prove that all Galerkin truncations of the 2d stochastic Navier-Stokes equations in vorticity form on any rectangular torus subjected to hypoelliptic, additive stochastic forcin…
A regularity method for lower bounds on the Lyapunov exponent for stochastic differential equations
Jacob Bedrossian, Alex Blumenthal, Sam Punshon-Smith
We put forward a new method for obtaining quantitative lower bounds on the top Lyapunov exponent of stochastic differential equations (SDEs). Our method combines (i) an (apparently…
Almost-sure enhanced dissipation and uniform-in-diffusivity exponential mixing for advection-diffusion by stochastic Navier-Stokes
Jacob Bedrossian, Alex Blumenthal, Samuel Punshon-Smith
We study the mixing and dissipation properties of the advection-diffusion equation with diffusivity and advection by a class of random velocity fields on …
The Batchelor spectrum of passive scalar turbulence in stochastic fluid mechanics at fixed Reynolds number
Jacob Bedrossian, Alex Blumenthal, Sam Punshon-Smith
In 1959, Batchelor predicted that the stationary statistics of passive scalars advected in fluids with small diffusivity should display a power spectrum along an ine…
Almost-sure exponential mixing of passive scalars by the stochastic Navier-Stokes equations
Jacob Bedrossian, Alex Blumenthal, Samuel Punshon-Smith
We deduce almost-sure exponentially fast mixing of passive scalars advected by solutions of the stochastically-forced 2D Navier-Stokes equations and 3D hyper-viscous Navier-Stokes…
Sufficient conditions for dual cascade flux laws in the stochastic 2d Navier-Stokes equations
Jacob Bedrossian, Michele Coti Zelati, Sam Punshon-Smith +1
We provide sufficient conditions for mathematically rigorous proofs of the third order universal laws capturing the energy flux to large scales and enstrophy flux to small scales f…
Lagrangian chaos and scalar advection in stochastic fluid mechanics
Jacob Bedrossian, Alex Blumenthal, Samuel Punshon-Smith
We study the Lagrangian flow associated to velocity fields arising from various models of fluid mechanics subject to white-in-time, -in-space stochastic forcing in a periodic…
A sufficient condition for the Kolmogorov 4/5 law for stationary martingale solutions to the 3D Navier-Stokes equations
Jacob Bedrossian, Michele Coti Zelati, Samuel Punshon-Smith +1
We prove that statistically stationary martingale solutions of the 3D Navier-Stokes equations on subjected to white-in-time (colored-in-space) forcing satisfy the Ko…
Renormalized Solutions to Stochastic Continuity Equations with Rough Coefficients
Samuel Punshon-Smith
We consider the stochastic continuity equation associated to an Itô diffusion with irregular drift and diffusion coefficients. We give regularity conditions under which weak soluti…
On the Boltzmann Equation with Stochastic Kinetic Transport: Global Existence of Renormalized Martingale Solutions
Samuel Punshon-Smith, Scott Smith
This article studies the Cauchy problem for the Boltzmann equation with stochastic kinetic transport. Under a cut-off assumption on the collision kernel and a coloring hypothesis f…