73 citations · 315 across the 46 of their papers we have counts for
53 papers
Dynamics of Ideal Fluid Flows
Tarek M. Elgindi
We will discuss various aspects of the incompressible Euler equation. We will discuss, in particular, problems related to the least action principle, the existence of special solut…
On the existence of fibered three-dimensional perfect fluid equilibria without continuous Euclidean symmetry
Theodore D. Drivas, Tarek M. Elgindi, Daniel Ginsberg
Following Lortz, we construct a family of smooth steady states of the ideal, incompressible Euler equation in three dimensions that possess no continuous Euclidean symmetry. As in…
A Classification Theorem for Steady Euler Flows
Tarek M. Elgindi, Yupei Huang, Ayman R. Said +1
Fix a bounded, analytic, and simply connected domain We show that all analytic steady states of the Euler equations with stream function are either radi…
Finite-time singularity formation for scalar stretching equations
Roberta Bianchini, Tarek M. Elgindi
We consider equations of the type: \[\partial_t ω= ωR(ω),\] for general linear operators in any spatial dimension. We prove that such equations almost always exhibit finite-tim…
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…
On the long-time behavior of scale-invariant solutions to the 2d Euler equation and applications
Tarek. M. Elgindi, Ryan. W. Murray, Ayman. R. Said
We study the long-time behavior of scale-invariant solutions of the 2d Euler equation satisfying a discrete symmetry. We show that all scale-invariant solutions with bounded variat…
Strong Ill-Posedness in for the Riesz Transform Problem
Tarek M. Elgindi, Karim R. Shikh Khalil
We prove strong ill-posedness in for linear perturbations of the 2d Euler equations of the form: \[\partial_t ω+ u\cdot\nablaω= R(ω),\] where is any non-trivial se…
Regular and Singular Steady States of 2D incompressible Euler equations near the Bahouri-Chemin Patch
Tarek M. Elgindi, Yupei Huang
We consider steady states of the two-dimensional incompressible Euler equations in and construct smooth and singular steady states around a particular singular stead…
Propagation of singularities by Osgood vector fields and for 2D inviscid incompressible fluids
Theodore D. Drivas, Tarek M. Elgindi, Joonhyun La
We show that certain singular structures (Hölderian cusps and mild divergences) are transported by the flow of homeomorphisms generated by an Osgood velocity field. The structure o…
Singularity formation in the incompressible Euler equation in finite and infinite time
Theodore D. Drivas, Tarek M. Elgindi
Some classical and recent results on the Euler equations governing perfect (incompressible and inviscid) fluid motion are collected and reviewed, with some small novelties scattere…
Growth of Sobolev norms and loss of regularity in transport equations
Gianluca Crippa, Tarek Elgindi, Gautam Iyer +1
We consider transport of a passive scalar advected by an irregular divergence free vector field. Given any non-constant initial data , $d\g…
Stationary Structures near the Kolmogorov and Poiseuille Flows in the 2d Euler Equations
Michele Coti Zelati, Tarek M. Elgindi, Klaus Widmayer
We study the behavior of solutions to the incompressible Euler equations near two canonical shear flows with critical points, the Kolmogorov and Poiseuille flows, with consequ…
WaveQ: Gradient-Based Deep Quantization of Neural Networks through Sinusoidal Adaptive Regularization
Ahmed T. Elthakeb, Prannoy Pilligundla, Fatemehsadat Mireshghallah +3
As deep neural networks make their ways into different domains, their compute efficiency is becoming a first-order constraint. Deep quantization, which reduces the bitwidth of the…
The incompressible Euler equations under octahedral symmetry: singularity formation in a fundamental domain
Tarek M. Elgindi, In-Jee Jeong
We consider the 3D incompressible Euler equations in vorticity form in the following fundamental domain for the octahedral symmetry group: In…
Anomalous Dissipation in Passive Scalar Transport
Theodore D. Drivas, Tarek M. Elgindi, Gautam Iyer +1
We study anomalous dissipation in hydrodynamic turbulence in the context of passive scalars. Our main result produces an incompressible $C^\infty([0,T)\times \mathbb{T}^d)\cap L^1(…
On the Stability of Self-similar Blow-up for Solutions to the Incompressible Euler Equations on
Tarek M. Elgindi, Tej-Eddine Ghoul, Nader Masmoudi
We study the stability of recently constructed self-similar blow-up solutions to the incompressible Euler equation. A consequence of our work is the existence of finite-energy $C^{…
On Singular Vortex Patches, II: Long-time dynamics
Tarek M. Elgindi, In-Jee Jeong
In a companion paper, we gave a detailed account of the well-posedness theory for singular vortex patches. Here, we discuss the long-time dynamics of some of the classes of vortex…
Inviscid limit of vorticity distributions in Yudovich class
Peter Constantin, Theodore D. Drivas, Tarek M. Elgindi
We prove that given initial data , forcing , and any , the solutions of Navier-Stokes converge…