73 citations · 315 across the 46 of their papers we have counts for
7 papers · 2 filters
Asymptotic Stability for some Stratified Stationary Solutions of the Inviscid Incompressible Porous Medium Equation
Tarek M. Elgindi
We initiate the study of stability of solutions of the 2D inviscid incompressible porous medium equation (IPM). We begin by classifying all stationary solutions of the inviscid IPM…
Sharp decay estimates for an anisotropic linear semigroup and applications to the SQG and inviscid Boussinesq systems
Tarek M. Elgindi, Klaus Widmayer
At the core of this article is an improved, sharp dispersive estimate for the anisotropic linear semigroup arising in both the study of the dispersive SQG equation and…
Sharp L^p estimates for singular transport equations
Tarek M. Elgindi
We prove sharp estimates for a singular transport equation by building what we call a \emph{cascading solution}; the equation studies the combined effect of multiplying by a…
Note on the Euler equations in C^k spaces
Tarek M. Elgindi, Nader Masmoudi
In this note, using the ideas from our recent article \cite{EM}, we prove strong ill-posedness for the 2D Euler equations in spaces. This note provides a significantly shorte…
Ill-posedness results in critical spaces for some equations arising in hydrodynamics
Tarek M. Elgindi, Nader Masmoudi
Many questions related to well-posedness/ill-posedness in critical spaces for hydrodynamic equations have been open for many years. In this article we give a new approach to studyi…
Uniform Regularity for free-boundary navier-stokes equations with surface tension
Tarek Elgindi, Donghyun Lee
We study the zero-viscosity limit of free boundary Navier-Stokes equations with surface tension in thus extending the work of Masmoudi and Rousset [1] to take surfac…
On the inviscid limit of the 2D Euler equations with vorticity along the scale
Frederic Bernicot, Tarek M. Elgindi, Sahbi Keraani
In a recent paper [5], the global well-posedness of the two-dimensional Euler equation with vorticity in \mbox{} was proved, where is a Banach space which is…