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math.AP2022
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…
math.AP2014★ 1 cited
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…
math.AP2014
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…