2 citations · 2 across the 5 of their papers we have counts for
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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…