Publications

2d Incompressible Euler equations

A Classification Theorem for Steady Euler Flows
Tarek M. Elgindi, Yupei Huang, Ayman R. Said, Chunjing Xie. arXiv preprint 2024.

Small scale creation of the Lagrangian flow in 2d perfect fluids
Ayman R. Said. arXiv preprint 2024.

Wellposedness and singularity formation beyond the Yudovich class
Tarek. M. Elgindi, Ryan M. Muray, Ayman R. Said. arXiv preprint 2023.

Logarithmic spirals in 2d perfect fluids
In-Jee Jeong, Ayman R. Said. Journal de l’École polytechnique — Mathématiques, 2024.

On the long-time behavior of scale-invariant solutions to the 2d Euler equation and applications
Tarek. M. Elgindi, Ryan M. Muray, Ayman R. Said. To appear in Les Annales de l’ENS, 2025.

ODEs with Sobolev vector fields

A quantitative DiPerna-Lions theory and exponential mixing rate for passive scalar transport
L. Huysmans, Ayman R. Said. arXiv preprint 2024.

The regularity of the solution map of the water waves system and the dispersive Burgers equation

Regularity results on the flow maps of periodic dispersive Burgers type equations and the Gravity-Capillary equations
Ayman R. Said. Water Waves, 2023.

A geometric proof of the quasi-linearity of the water-waves system
Ayman R. Said. Indiana University Mathematics Journal, 2023.

The Cauchy problem of the dispersive Burgers equation

On the Cauchy problem of dispersive Burgers type equations
Ayman R. Said. SIAM Journal on Mathematical Analysis, 2023.

Paradifferential Calculus

On paracomposition and change of variables in paradifferential operators
Ayman R. Said. Journal of Pseudo-Differential Operators and Applications, 2023.

Thesis

Sur le flot de l’équation d’Euler à surface libre
Ayman R. Said. Hal 2021.