167 citations · 623 across the 43 of their papers we have counts for
18 papers · 1 filter
Unique Ergodicity in Stochastic Electroconvection
Elie Abdo, Nathan Glatt-Holtz, Mihaela Ignatova
We consider a stochastic electroconvection model describing the nonlinear evolution of a surface charge density in a two-dimensional fluid with additive stochastic forcing. We prov…
Affine Poisson & Non-Poisson trace principles for
Nico Lombardi, Jie Xiao
This note discovers not only an affine non-sharp-Poisson trace inequality but also its sharp-non-Poisson version for a Sobolev function with the fractional antiderivative.
Invariant measures for the stochastic one-dimensional compressible Navier-Stokes equations
Michele Coti Zelati, Nathan Glatt-Holtz, Konstantina Trivisa
We investigate the long-time behavior of solutions to a stochastically forced one-dimensional Navier-Stokes system, describing the motion of a compressible viscous fluid, in the ca…
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…
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…
Invariant measures for passive scalars in the small noise inviscid limit
Jacob Bedrossian, Michele Coti Zelati, Nathan Glatt-Holtz
We consider a class of invariant measures for a passive scalar driven by an incompressible velocity field , on a -dimensional periodic domain, satisfying $$…
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…
Time Discrete Approximation of Weak Solutions for Stochastic Equations of Geophysical Fluid Dynamics and Applications
Nathan Glatt-Holtz, Roger Temam, Chuntian Wang
As a first step towards the numerical analysis of the stochastic primitive equations of the atmosphere and oceans, we study their time discretization by an implicit Euler scheme. F…
Existence and Regularity of Invariant Measures for the Three Dimensional Stochastic Primitive Equations
Nathan Glatt-Holtz, Igor Kukavica, Vlad Vicol +1
We establish the continuity of the Markovian semigroup associated with strong solutions of the stochastic 3D Primitive Equations, and prove the existence of an invariant measure. T…
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…
Martingale and Pathwise Solutions to the Stochastic Zakharov-Kuznetsov Equation with Multiplicative Noise
Nathan Glatt-Holtz, Roger Temam, Chuntian Wang
We study in this article the stochastic Zakharov-Kuznetsov equation driven by a multiplicative noise. We establish, in space dimensions two and three the global existence of martin…
Unique Ergodicity for Fractionally Dissipated, Stochastically Forced 2D Euler Equations
Peter Constantin, Nathan Glatt-Holtz, Vlad Vicol
We establish the existence and uniqueness of an ergodic invariant measure for 2D fractionally dissipated stochastic Euler equations on the periodic box, for any power of the dissip…
On Inviscid Limits for the Stochastic Navier-Stokes Equations and Related Models
Nathan Glatt-Holtz, Vladimir Sverak, Vlad Vicol
We study inviscid limits of invariant measures for the 2D Stochastic Navier-Stokes equations. As shown in \cite{Kuksin2004} the noise scaling is the only one which leads…
Local and global existence of smooth solutions for the stochastic Euler equations with multiplicative noise
Nathan E. Glatt-Holtz, Vlad C. Vicol
We establish the local existence of pathwise solutions for the stochastic Euler equations in a three-dimensional bounded domain with slip boundary conditions and a very general non…
Global Existence and Regularity for the 3D Stochastic Primitive Equations of the Ocean and Atmosphere with Multiplicative White Noise
Arnaud Debussche, Nathan Glatt-Holtz, Roger Temam +1
The Primitive Equations are a basic model in the study of large scale Oceanic and Atmospheric dynamics. These systems form the analytical core of the most advanced General Circulat…
Pathwise Solutions of the 2D Stochastic Primitive Equations
Nathan Glatt-Holtz, Roger Temam
In this work we consider a stochastic version of the Primitive Equations (PEs) of the ocean and the atmosphere and establish the existence and uniqueness of pathwise, strong soluti…
Local Martingale and Pathwise Solutions for an Abstract Fluids Model
Arnaud Debussche, Nathan Glatt-Holtz, Roger Temam
We establish the existence and uniqueness of both local martingale and local pathwise solutions of an abstract nonlinear stochastic evolution system. The primary application of thi…
Asymptotics of the Coleman-Gurtin model
Mickaël D. Chekroun, Francesco Di Plinio, Nathan E. Glatt-Holtz +1
This paper is concerned with the integrodifferential equation $$\partial_t u-Δu -\int_0^\infty κ(s)Δu(t-s)\,\d s + φ(u)=f$$ arising in the Coleman-Gurtin's theory of heat conductio…