49 citations · 83 across the 8 of their papers we have counts for
12 papers
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…
Error propagation dynamics of PIV-based pressure field calculation (3): What is the minimum resolvable pressure in a reconstructed field?
Mingyuan Nie, Jared P. Whitehead, Geordie Richards +2
An analytical framework for the propagation of velocity errors into PIV-based pressure calculation is extended. Based on this framework, the optimal spatial resolution and the corr…
Hydrodynamic stability in the presence of a stochastic forcing:a case study in convection
Juraj Földes, Nathan Glatt-Holtz, Geordie Richards +1
We investigate the stability of statistically stationary conductive states for Rayleigh-Bénard convection that arise due to a bulk stochastic internal heating. Our results indicate…
Asymptotic Analysis for Randomly Forced MHD
Juraj Földes, Susan Friedlander, Nathan Glatt-Holtz +1
We consider the three-dimensional magnetohydrodynamics (MHD) equations in the presence of a spatially degenerate stochastic forcing as a model for magnetostrophic turbulence in the…
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…
Ergodicity in Randomly Forced Rayleigh-Bénard Convection
J. Földes, N. Glatt-Holtz, G. Richards +1
We consider the Boussinesq approximation for Rayleigh-Bénard convection perturbed by an additive noise and with boundary conditions corresponding to heating from below. In two spac…
On invariant Gibbs measures for the generalized KdV equations
Tadahiro Oh, Geordie Richards, Laurent Thomann
We consider the defocusing generalized KdV equations on the circle. In particular, we construct global-in-time solutions with initial data distributed according to the Gibbs measur…
Large Prandtl Number Asymptotics in Randomly Forced Turbulent Convection
Juraj Foldes, Nathan Glatt-Holtz, Geordie Richards
We establish the convergence of statistically invariant states for the stochastic Boussinesq Equations in the infinite Prandtl number limit and in particular demonstrate the conver…
Ergodic and Mixing Properties of the Boussinesq Equations with a Degenerate Random Forcing
Juraj Földes, Nathan Glatt-Holtz, Geordie Richards +1
We establish the existence, uniqueness and attraction properties of an ergodic invariant measure for the Boussinesq Equations in the presence of a degenerate stochastic forcing act…
Invariance of the Gibbs measure for the periodic quartic gKdV
Geordie Richards
We prove invariance of the Gibbs measure for the (gauge transformed) periodic quartic gKdV. The Gibbs measure is supported on H^s for s<1/2, and the quartic gKdV is analytically il…
Local and global well-posedness of the stochastic KdV-Burgers equation
Geordie Richards
The stochastic PDE known as the Kardar-Parisi-Zhang equation (KPZ) has been proposed as a model for a randomly growing interface. This equation can be reformulated as a stochastic…
Mass Concentration for the Davey-Stewartson System
Geordie Richards
This paper is concerned with the analysis of blow-up solutions to the elliptic-elliptic Davey-Stewartson system, which appears in the description of the evolution of surface water…