131 citations · 233 across the 19 of their papers we have counts for
25 papers
On Galerkin approximations of the Navier-Stokes equations in the limit of large Grashof numbers
Ciprian Foias, Luan Hoang, Michael S. Jolly
We examine how stationary solutions to Galerkin approximations of the Navier--Stokes equations behave in the limit as the Grashof number tends to . An appropriate scali…
Convergence of a mobile data assimilation scheme for the 2D Navier-Stokes equations
Animikh Biswas, Zachary Bradshaw, Michael Jolly
We introduce a localized version of the nudging data assimilation algorithm for the periodic 2D Navier-Stokes equations in which observations are confined (i.e., localized) to a wi…
Data Assimilation with Higher Order Finite Element Interpolants
Michael S. Jolly, Ali Pakzad
The efficacy of a nudging data assimilation algorithm using higher order finite element interpolating operators is studied. Numerical experiments are presented for the 2D Navier-St…
Continuous Data Assimilation For the 3D Ladyzhenskaya Model: Analysis and Computations
Yu Cao, Andrea Giorgini, Michael Jolly +1
We analyze continuous data assimilation by nudging for the 3D Ladyzhenskaya equations. The analysis provides conditions on the spatial resolution of the observed data that guarante…
On local well-posedness of logarithmic inviscid regularizations of generalized SQG equations in borderline Sobolev spaces
Michael S. Jolly, Anuj Kumar, Vincent R. Martinez
This paper studies a family of generalized surface quasi-geostrophic (SQG) equations for an active scalar on the whole plane whose velocities have been mildly regularized, for…
On the existence, uniqueness, and smoothing of solutions to the generalized SQG equations in critical Sobolev spaces
Michael S. Jolly, Anuj Kumar, Vincent R. Martinez
This paper studies the dissipative generalized surface quasi-geostrophic equations in a supercritical regime where the order of the dissipation is small relative to order of the ve…
Three-dimensional shear driven turbulence with noise at the boundary
Wai-Tong Louis Fan, Michael Jolly, Ali Pakzad
We consider the incompressible 3D Navier-Stokes equations subject to a shear induced by noisy movement of part of the boundary. The effect of the noise is quantified by upper bound…
Data assimilation for the Navier-Stokes equations using local observables
Animikh Biswas, Zachary Bradshaw, Michael S. Jolly
We develop, analyze, and test an approximate, global data assimilation/synchronization algorithm based on purely local observations for the two-dimensional Navier-Stokes equations…
A Determining Form for the 2D Rayleigh-Bénard Problem
Yu Cao, Michael S. Jolly, Edriss S. Titi
We construct a determining form for the 2D Rayleigh-Bénard (RB) system in a strip with solid horizontal boundaries, in the cases of no-slip and stress-free boundary conditions. The…
Algebraic Bounds on the Rayleigh-Bénard attractor
Yu Cao, Michael S. Jolly, Edriss S. Titi +1
The Rayleigh-Bénard system with stress-free boundary conditions is shown to have a global attractor in each affine space where velocity has fixed spatial average. The physical prob…
Continuous data assimilation with blurred-in-time measurements of the surface quasi-geostrophic equation
Michael S. Jolly, Vincent R. Martinez, Eric J. Olson +1
An intrinsic property of almost any physical measuring device is that it makes observations which are slightly blurred in time. We consider a nudging-based approach for data assimi…
Assimilation of nearly turbulent Rayleigh-Bénard flow through vorticity or local circulation measurements: a computational study
Aseel Farhat, Hans Johnston, Michael S. Jolly +1
We introduce a continuous (downscaling) data assimilation algorithm for the 2D Bénard convection problem using vorticity or local circulation measurements only. In this algorithm,…
A determining form for the subcritical surface quasi-geostrophic equation
Michael S. Jolly, Vincent R. Martinez, Tural Sadigov +1
We construct a determining form for the surface quasi-geostrophic (SQG) equation with subcritical dissipation. In particular, we show that the global attractor for this equation ca…
Energy spectra and passive tracer cascades in turbulent flows
Michael Jolly, Djoko Wirosoetisno
We study the influence of the energy spectrum on the extent of the cascade range of a passive tracer in turbulent flows. The interesting cases are when there are two different spec…
A data assimilation algorithm for the subcritical surface quasi-geostrophic equation
Michael S. Jolly, Vincent R. Martinez, Edriss S. Titi
In this article, we prove that data assimilation by feedback nudging can be achieved for the three-dimensional quasi-geostrophic equation in a simplified scenario using only large…
One-dimensional parametric determining form for the two-dimensional Navier-Stokes equations
Ciprian Foias, Michael S. Jolly, Daniel Lithio +1
The evolution of a determining form for the 2D Navier-Stokes equations (NSE), which is an ODE on a space of trajectories is completely described. It is proved that at every stage o…
Determining form and data assimilation algorithm for weakly damped and driven Korteweg-de Vries equaton- Fourier modes case
Michael S. Jolly, Tural Sadigov, Edriss S. Titi
We show that the global attractor of a weakly damped and driven Korteweg-de Vries equation (KdV) is embedded in the long-time dynamics of an ordinary differential equation called a…
Continuous Data Assimilation for the 2D Bénard Convection through Velocity Measurements Alone
Aseel Farhat, Michael S. Jolly, Edriss S. Titi
An algorithm for continuous data assimilation for the two- dimensional Bénard convection problem is introduced and analyzed. It is inspired by the data assimilation algorithm devel…
A determining form for the damped driven Nonlinear Schrödinger Equation- Fourier modes case
Michael S. Jolly, Tural Sadigov, Edriss S. Titi
In this paper we show that the global attractor of the 1D damped, driven, nonlinear Schrödinger equation (NLS) is embedded in the long-time dynamics of a determining form. The dete…
On whether zero is in the global attractor of the 2D Navier-Stokes equations
Ciprian Foias, Michael Jolly, Yong Yang +1
The set of nonzero external forces for which the zero function is in the global attractor of the 2D Navier-Stokes equations is shown to be meagre in a Fréchet topology. A criterion…
Time analyticity with higher norm estimates for the 2D Navier-Stokes equations
Ciprian Foias, Michael S. Jolly, Ruomeng Lan +3
This paper establishes bounds on norms of all orders for solutions on the global attractor of the 2D Navier-Stokes equations, complexified in time. Specifically, for periodic bound…
Dissipative length scale estimates for turbulent flows - a Wiener algebra approach
Animikh Biswas, Michael S. Jolly, Vincent R. Martinez +1
In this paper, a lower bound estimate on the uniform radius of spatial analyticity is established for solutions to the incompressible, forced Navier-Stokes system on an n-torus. Th…
A unified approach to determining forms for the 2D Navier-Stokes equations - the general interpolants case
Ciprian Foias, Michael S. Jolly, Rostyslav Kravchenko +1
In this paper we show that the long time dynamics (the global attractor) of the 2D Navier-Stokes equation is embedded in the long time dynamics of an ordinary differential equation…
A unified approach to compute foliations, inertial manifolds, and tracking initial conditions
Y. -M. Chung, M. S. Jolly
Several algorithms are presented for the accurate computation of the leaves in the foliation of an ODE near a hyperbolic fixed point. They are variations of a contraction mapping m…