6 papers
Kinetic shock profiles for the Landau equation
Dallas Albritton, Jacob Bedrossian, Matthew Novack
The physical quantities in a gas should vary continuously across a shock. However, the physics inherent in the compressible Euler equations is insufficient to describe the width or…
Forward self-similar solutions to the 2D Navier--Stokes equations
Dallas Albritton, Julien Guillod, Mikhail Korobkov +1
We construct self-similar solutions to the 2D Navier--Stokes equations evolving from arbitrarily large --homogeneous initial data and present numerical evidence for their non-u…
Linear and nonlinear instability of vortex columns
Dallas Albritton, Wojciech OżaÅski
We consider vortex column solutions to the D Euler equations. We give a mathematically rigorous construction of the countable family of unstable modes…
Sharp uniform-in-diffusivity mixing rates for passive scalars in parallel shear flows
Dallas Albritton, Rajendra Beekie
We consider the advection-diffusion equation describing the evolution of a passive scalar in a background shear flow. We prove the optimal uniform-in-diffusivity mixing rate $\| f…
Vanishing viscosity non-unique solutions to the forced 2D Euler Equations
Dallas Albritton, Maria Colombo, Giulia Mescolini
The forced 2D Euler equations exhibit non-unique solutions with vorticity in , , whereas the corresponding Navier-Stokes solutions are unique. We investigate whether th…
Rods in flows: the PDE theory of immersed elastic filaments
Dallas Albritton, Laurel Ohm
We investigate a family of curve evolution equations approximating the motion of a Kirchhoff rod immersed in a low Reynolds number fluid. The rod is modeled as a framed curve whose…