16 citations · 43 across the 22 of their papers we have counts for
29 papers
Local separation profiles for the stationary Prandtl system
Ky Giao Duong, Tej-Eddine Ghoul, Sameer Iyer +1
We construct solutions to the two-dimensional stationary Prandtl system under a constant adverse pressure gradient exhibiting a family of distinct separation laws. More precisely,…
Blow-up of the one-dimensional wave equation with quadratic spatial derivative nonlinearity
Tej-eddine Ghoul, Jie Liu, Nader Masmoudi
We investigate the blow-up dynamics of smooth solutions to the one-dimensional wave equation with a quadratic spatial derivative nonlinearity, motivated by its applications in Effe…
Singularity formed by the collision of two collapsing solitons in interaction for the 2D Keller-Segel system
Charles Collot, Tej-Eddine Ghoul, Nader Masmoudi +1
It is well-known that the two-dimensional parabolic-elliptic Keller-Segel system admits finite-time blowup solutions, which is the case if the initial density has total mass greate…
Blow-Up Dynamics for the critical case of the D Zakharov-Kuznetsov equation
Francisc Bozgan, Tej-Eddine Ghoul, Nader Masmoudi +1
We study blow-up dynamics for the -critical cubic Zakharov--Kuznetsov equation in two dimensions, \[ \partial_tu+\partial_{x_1}(Δu+u^3)=0 \qquad\text{on }\mathbb R^2. \] For a…
Nonlinear enhanced dissipation in viscous Burgers type equations II
Tej-Eddine Ghoul, Nader Masmoudi, Eliot Pacherie
In this follow up paper, we focus on the viscous Burgers equation. There, using the Hopf-Cole transformation, we compute the long time behavior of solutions for some classes of inf…
Nonlinear enhanced dissipation in viscous Burgers type equations
Tej-Eddine Ghoul, Nader Masmoudi, Eliot Pacherie
We construct a class of infinite mass functions for which solutions of the viscous Burgers equation decay at a better rate than solution of the heat equation for initial data in th…
Localisation of perturbations of a constant state in a traffic flow model
Tej-Eddine Ghoul, Nader Masmoudi, Eliot Pacherie
We consider, in the Aw-Rascle-Zhang traffic flow model, the problem of the asymptotic stability of constant flows. By using a perturbative approach, we show the stability in a larg…
Non-self similar blowup solutions to the higher dimensional Yang-Mills heat flows
A. Bensouilah, G. K. Duong, T. E. Ghoul
In this paper, we consider the Yang-Mills heat flow on with . Under a certain symmetry preserved by the flow, the Yang-Mills equation can be re…
Collapsing-ring blowup solutions for the Keller-Segel system in three dimensions and higher
Charles Collot, Tej-Eddine Ghoul, Nader Masmoudi +1
We consider the parabolic-elliptic Keller-Segel system in three dimensions and higher, corresponding to the mass supercritical case. We construct rigorously a solution which blows…
Blowup solutions for the shadow limit model of singular Gierer-Meinhardt system with critical parameters
G. K. Duong, T. E. Ghoul, N. I. Kavallaris +1
We consider a nonlocal parabolic PDE, which may be regarded as the standard semilinear heat equation with power nonlinearity, where the nonlinear term is divided by some Sobolev no…
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…
Construction and Stability of type I blowup solutions for non-variational semilinear parabolic systems
Tej-Eddine Ghoul, Van Tien Nguyen, Hatem Zaag
We consider in this note the semilinear heat system where the nonlinearity has no gradient structure taki…
On singularity formation for the two dimensional unsteady Prandtl system around the axis
Charles Collot, Tej-Eddine Ghoul, Slim Ibrahim +1
We consider the two dimensional unsteady Prandtl system. For a special class of outer Euler flows and solutions of the Prandtl system, the trace of the tangential derivative of the…
Construction of type I blowup solutions for a higher order semilinear parabolic equation
Tej-Eddine Ghoul, Van Tien Nguyen, Hatem Zaag
We consider the higher-order semilinear parabolic equation in the whole space , where and is an odd…
Singularity formation for Burgers equation with transverse viscosity
Charles Collot, Tej-Eddine Ghoul, Nader Masmoudi
We consider Burgers equation with transverse viscosity …
Stable type II blowup for the 7 dimensional 1-corotational energy supercritical harmonic map heat flow
Tej-eddine Ghoul
We consider the energy-supercritical harmonic map heat flow from into , under an additional assumption of 1-corotational symmetry. We are interested by…
Blowup solutions for a reaction-diffusion system with exponential nonlinearities
Tej-Eddine Ghoul, Van Tien Nguyen, Hatem Zaag
We consider the following parabolic system whose nonlinearity has no gradient structure: $$\left\{\begin{array}{ll} \partial_t u = Δu + e^{pv}, \quad & \partial_t v = μΔv + e^{qu},…
Construction of type II blowup solutions for the 1-corotational energy supercritical wave maps
Tej-Eddine Ghoul, Slim Ibrahim, Van Tien Nguyen
We consider the energy supercritical wave maps from into the -sphere with . Under an additional assumption of 1-corotational symmetry, th…
Blowup solutions for a nonlinear heat equation involving a critical power nonlinear gradient term
Tej-Eddine Ghoul, Van Tien Nguyen, Hatem Zaag
We consider the following exponential reaction-diffusion equation involving a nonlinear gradient term: $$\partial_t U = ΔU + α|\nabla U|^2 + e^U,\quad (x, t)\in\mathbb{R}^N\times[0…
On the stability of type II blowup for the 1-corotational energy supercritical harmonic heat flow
Tej-Eddine Ghoul, Slim Ibrahim, Van Tien Nguyen
We consider the energy supercritical harmonic heat flow from into the -sphere with . Under an additional assumption of 1-corotational sym…