18 citations · 34 across the 8 of their papers we have counts for
10 papers
Optimal Linear Inviscid Damping and Vorticity Depletion for Non-monotonic shear flows
Rajendra Beekie, Shan Chen, Hao Jia
We give a proof of optimal pointwise linear inviscid damping and vorticity depletion for a large class of spectrally stable shear flows on the rectangular torus. This extend…
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…
Uniform vorticity depletion and inviscid damping for periodic shear flows in the high Reynolds number regime
Rajendra Beekie, Shan Chen, Hao Jia
We study the dynamics of the two dimensional Navier-Stokes equations linearized around a shear flow on a (non-square) torus which possesses exactly two non-degenerate critical poin…
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…
On Moffatt's magnetic relaxation equations
Rajendra Beekie, Susan Friedlander, Vlad Vicol
We investigate the stability properties for a family of equations introduced by Moffatt to model magnetic relaxation. These models preserve the topology of magnetic streamlines, co…
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…
Universal wavenumber selection laws in apical growth
Ryan Goh, Rajendra Beekie, Daniel Matthias +2
We study pattern-forming dissipative systems in growing domains. We characterize classes of boundary conditions that allow for defect-free growth and derive universal scaling laws…