16 citations · 43 across the 22 of their papers we have counts for
5 papers · 1 filter
Refined description and stability for singular solutions of the 2D Keller-Segel system
Charles Collot, Tej-Eddine Ghoul, Nader Masmoudi +1
We construct solutions to the two dimensional parabolic-elliptic Keller-Segel model for chemotaxis that blow up in finite time . The solution is decomposed as the sum of a stati…
Spectral analysis for singularity formation of the two dimensional Keller-Segel system
Charles Collot, Tej-Eddine Ghoul, Nader Masmoudi +1
We analyse an operator arising in the description of singular solutions to the two-dimensional Keller-Segel problem. It corresponds to the linearised operator in parabolic self-sim…
On the Stability of Self-similar Blow-up for Solutions to the Incompressible Euler Equations on
Tarek M. Elgindi, Tej-Eddine Ghoul, Nader Masmoudi
We study the stability of recently constructed self-similar blow-up solutions to the incompressible Euler equation. A consequence of our work is the existence of finite-energy $C^{…
Stable self-similar blowup for a family of nonlocal transport equations
Tarek M. Elgindi, Tej-Eddine Ghoul, Nader Masmoudi
We consider a family of non-local problems that model the effects of transport and vortex stretching in the incompressible Euler equations. Using modulation techniques, we establis…
Singularities and unsteady separation for the inviscid two-dimensional Prandtl's system
Charles Collot, Tej-Eddine Ghoul, Nader Masmoudi
We consider the inviscid unsteady Prandtl system in two dimensions, motivated by the fact that it should model to leading order separation and singularity formation for the origina…