2 citations · 2 across the 3 of their papers we have counts for
6 papers
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…
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…
Navier-Stokes equations, determining forms, determining modes, inertial manifolds, dissipative dynamical systems
Ciprian Foias, Michael S. Jolly, Rostyslav Kravchenko +1
The determining modes for the two-dimensional incompressible Navier-Stokes equations (NSE) are shown to satisfy an ordinary differential equation of the form , in the B…