73 citations · 315 across the 46 of their papers we have counts for
5 papers · 2 filters
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…