73 citations · 315 across the 46 of their papers we have counts for
7 papers · 1 filter
Wellposedness and singularity formation beyond the Yudovich class
Tarek M. Elgindi, Ryan W. Murray, Ayman R. Said
We introduce a local-in-time existence and uniqueness class for solutions to the 2d Euler equation with unbounded vorticity. Furthermore, we show that solutions belonging to this c…
From Instability to Singularity Formation in Incompressible Fluids
Tarek M. Elgindi, Federico Pasqualotto
We establish finite-time singularity formation for solutions to the Boussinesq system that are compactly supported on and infinitely smooth except in the r…
Invertibility of a linearized Boussinesq flow: a symbolic approach
Tarek M. Elgindi, Federico Pasqualotto
We develop a computer-assisted symbolic method to show that a linearized Boussinesq flow in self-similar coordinates gives rise to an invertible operator.
Norm Growth, Non-uniqueness, and Anomalous Dissipation in Passive Scalars
Tarek M. Elgindi, Kyle Liss
We construct a divergence-free velocity field satisfying such th…
Remark on the Stability of Energy Maximizers for the 2D Euler equation on
Tarek M. Elgindi
It is well-known that the first energy shell, \[\mathcal{S}_1^{c_0}:=\{α\cos(x+μ)+β\cos(y+λ): α^2+β^2=c_0\,\, \&\,\, (μ,λ)\in\mathbb{R}^2\}\] of solutions to the 2d Euler equation…
Twisting in Hamiltonian Flows and Perfect Fluids
Theodore D. Drivas, Tarek M. Elgindi, In-Jee Jeong
We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting…
Optimal enhanced dissipation and mixing for a time-periodic, Lipschitz velocity field on
Tarek M. Elgindi, Kyle Liss, Jonathan C. Mattingly
We consider the advection-diffusion equation on with a Lipschitz and time-periodic velocity field that alternates between two piecewise linear shear flows. We prove…