Publications

2d Incompressible Euler equations

Generic small-scale creation in the two-dimensional Euler equation
Thomas Alazard, Ayman R. Said, arXiv preprint 2026.

A Classification Theorem for Steady Euler Flows
Tarek M. Elgindi, Yupei Huang, Ayman R. Said. Duke Mathematical Journal, 2026.

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. Journal of the European Mathematical Society, 2026.

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. Les Annales de l’ENS, 2025.

3d Incompressible Euler equations

On smooth inviscid vortices with fat tails
Pierre Raphaël, Ayman R. Said, arXiv preprint 2026.

ODEs with Sobolev vector fields

Mixing Estimates for Passive Scalar Transport by BV Vector Fields
L. Huysmans, Ayman R. Said. arXiv preprint 2025.

A unified approach to mixing and regularity for passive scalar transport by Sobolev vector fields
L. Huysmans, Ayman R. Said. Journal of Functional Analysis, 2026.

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. SIAM Journal on Mathematical Analysis, 2023.

The Cauchy problem of the dispersive Burgers equation

On the Cauchy problem of dispersive Burgers type equations
Ayman R. Said. Indiana University Mathematics Journal, 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.