24 citations · 24 across the 2 of their papers we have counts for
5 papers
Determining modes for the 3D Navier-Stokes equations
Alexey Cheskidov, Mimi Dai, Landon Kavlie
We introduce a determining wavenumber for the forced 3D Navier-Stokes equations (NSE) defined for each individual solution. Even though this wavenumber blows up if the solution blo…
Gaining two derivatives on a singular force in the 2D Navier-Stokes equations
Alexey Cheskidov, Landon Kavlie
It has long been known, for the autonomous 2D Navier-Stokes equations with singular forcing, that there exist unique solutions which gain one derivative, globally. On the other han…
Stability of Vortex Solutions to an Extended Navier-Stokes System
Gung-Min Gie, Christopher Henderson, Gautam Iyer +2
We study the long-time behavior an extended Navier-Stokes system in where the incompressibility constraint is relaxed. This is one of several "reduced models" of Grubb and S…
Degenerate pullback attractors for the 3D Navier-Stokes equations
Alexey Cheskidov, Landon Kavlie
As in our previous paper, the 3D Navier-Stokes equations with a translationally bounded force contain pullback attractors in a weak sense. Moreover, those attractors consist of com…
Pullback Attractors for Generalized Evolutionary Systems
Alexey Cheskidov, Landon Kavlie
We give an abstract framework for studying nonautonomous PDEs, called a generalized evolutionary system. In this setting, we define the notion of a pullback attractor. Moreover, we…