167 citations · 623 across the 43 of their papers we have counts for
10 papers · 1 filter
Existence and higher regularity of statistically steady states for the stochastic Coleman-Gurtin equation
Nathan E. Glatt-Holtz, Vincent R. Martinez, Hung D. Nguyen
We study a class of semi-linear differential Volterra equations with polynomial-type potentials that incorporates the effects of memory while being subjected to random perturbation…
The short memory limit for long time statistics in a stochastic Coleman-Gurtin model of heat conduction
Nathan E. Glatt-Holtz, Vincent R. Martinez, Hung D. Nguyen
We consider a class of semi-linear differential Volterra equations with polynomial-type potentials that incorporates the effects of memory while being subjected to random perturbat…
On the long-time statistical behavior of smooth solutions of the weakly damped, stochastically-driven KdV equation
Nathan Glatt-Holtz, Vincent R. Martinez, Geordie H. Richards
This paper considers the damped periodic Korteweg-de Vries (KdV) equation in the presence of a white-in-time and spatially smooth stochastic source term and studies the long-time b…
Sensitivity of steady states in a degenerately-damped stochastic Lorenz system
Juraj Foldes, Nathan E. Glatt-Holtz, David P. Herzog
We study stability of solutions for a randomly driven and degenerately damped version of the Lorenz '63 model. Specifically, we prove that when damping is absent in one of the temp…
On the convergence of stationary solutions in the Smoluchowski-Kramers approximation of infinite dimensional systems
Sandra Cerrai, Nathan Glatt-Holtz
We prove the convergence, in the small mass limit, of statistically invariant states for a class of semi-linear damped wave equations, perturbed by an additive Gaussian noise, both…
The Generalized Langevin Equation with a power-law memory in a nonlinear potential well
Nathan Glatt-Holtz, David Herzog, Scott McKinley +1
The generalized Langevin equation (GLE) is a stochastic integro-differential equation that has been used to describe the velocity of microparticles in viscoelastic fluids. In this…
Scaling and Saturation in Infinite-Dimensional Control Problems with Applications to Stochastic Partial Differential Equations
Nathan E. Glatt-Holtz, David P. Herzog, Jonathan C. Mattingly
We establish the dual notions of scaling and saturation from geometric control theory in an infinite-dimensional setting. This generalization is applied to the low-mode control pro…
On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations
Nathan E. Glatt-Holtz, Jonathan C. Mattingly, Geordie Richards
We illustrate how the notion of asymptotic coupling provides a flexible and intuitive framework for proving the uniqueness of invariant measures for a variety of stochastic partial…
Notes on Statistically Invariant States in Stochastically Driven Fluid Flows
Nathan Glatt-Holtz
These expository notes address certain stationary and ergodic properties of the equations of fluid dynamics subject to a spatially degenerate (i.e. frequency localized), white in t…
Parameter Estimation for the Stochastically Perturbed Navier-Stokes Equations
Igor Cialenco, Nathan Glatt-Holtz
We consider a parameter estimation problem to determine the viscosity of a stochastically perturbed 2D Navier-Stokes system. We derive several different classes of estimators b…