2 citations · 2 across the 3 of their papers we have counts for
6 papers · 1 filter
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…
A PDE model for chemotaxis with logarithmic sensitivity and logistic growth
Padi Fuster Aguilera, Vincent R. Martinez, Kyle Kun Zhao
In this paper, we study the initial-boundary value problem and its asymptotic behavior for a repulsive chemotaxis model with logarithmic sensitivity and logistic growth. We establi…
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…
Asymptotic expansion for solutions of the Navier-Stokes equations with non-potential body forces
Luan T. Hoang, Vincent R. Martinez
We study the long-time behavior of spatially periodic solutions of the Navier-Stokes equations in the three-dimensional space. The body force is assumed to possess an asymptotic ex…
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…