4 citations · 4 across the 3 of their papers we have counts for
6 papers · 1 filter
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…
Transition Threshold for Strictly Monotone Shear Flows in Sobolev Spaces
Rajendra Beekie, Siming He
We study the stability of spectrally stable, strictly monotone, smooth shear flows in the 2D Navier-Stokes equations on with small viscosity . We…
Non-conservative solutions of the Euler- equations
Rajendra Beekie, Matthew Novack
The Euler- equations model the averaged motion of an ideal incompressible fluid when filtering over spatial scales smaller than . We show that there exists such that we…
Enhanced dissipation and Hörmander's hypoellipticity
Dallas Albritton, Rajendra Beekie, Matthew Novack
We examine the phenomenon of enhanced dissipation from the perspective of Hörmander's classical theory of second order hypoelliptic operators [31]. Consider a passive scalar in a s…
Long-time behavior of scalar conservation laws with critical dissipation
Dallas Albritton, Rajendra Beekie
The critical Burgers equation is a toy model for the competition between transport and diffusion with regard to shock formation in fluids.…
Weak solutions of ideal MHD which do not conserve magnetic helicity
Rajendra Beekie, Tristan Buckmaster, Vlad Vicol
We construct weak solutions to the ideal magneto-hydrodynamic (MHD) equations which have finite total energy, and whose magnetic helicity is not a constant function of time. In vie…