He studied in Tunis and then at the École normale supérieure in Paris with a diploma in 1996; In 1999 he received his doctorate from the University of Paris-Dauphine with Pierre-Louis Lions (Problemes asymptotiques en mecanique des fluides).
In 2013, together with his post-doctoral student Jacob Bedrossian, he strictly demonstrated the stability of the shear flow according to Couette for the two-dimensional Euler equations, i.e. in the non-linear case.
The stability in linear approximation was already proven by Lord Kelvin in 1887 and more precisely by William McFadden Orr in 1907.
He also obtained similar stability results in the viscous case for the boundary layer formation according to Prandtl in the two-dimensional Navier-Stokes equations (the linear theory is named here after Orr and Arnold Sommerfeld: Orr-Sommerfeld equations).
In 2022 he was awarded the International King Faisal Prize[4] jointly with Martin Hairer.