# ** ** I'M OUSSAMA LANDOULSI !

## ** ** Welcome to my web-page

I did my PhD thesis in Mathematics at university Sorbonne
Paris Nord (France).

I just successfully defended my PhD thesis in October 2020 !

Advisor: ** Prof.
Thomas Duyckaerts. **
**Address: **

99, avenue Jean-Baptiste Clément,

93430 – Villetaneuse-France

E-mail:**landoulsi@math.univ-paris13.fr **

### ** Research interest: **

My research interest is in dispersive partial differential equations,
studied from both pure and applied points of view.

My PhD research work deals with the nonlinear Schrödinger equation
NLS
in the exterior of a smooth, compact and convex obstacle.
The nonlinear Schrödinger equation combines the dispersive behavior of
the linear part of the equation with a nonlinearity.
The dynamics of the equation depends on the sign of the nonlienarity, which is typically of power type.
I am interested in the focusing (i.e, negative sign in front of the nonlinearity)
NLS equation, which has a richer and more involved dynamics due
to the opposite effects of the nonlinearity and the dispersion by Laplacian.
### ** Publications: **

- O. Landoulsi.
Construction of a solitary wave solution for the nonlinear
Schrödinger equation outside a convex obstacle in the L^2-supercritical case

Discrete Contin. Dyn. Syst. A (2021)

- T. Duyckaerts, O. Landoulsi and S. Roudenko.
Threshold solutions in the focusing 3D cubic NLS equation outside a strictly convex obstacle.
arXiv:2010.07724

- O. Landoulsi
On Blow-up solutions to the nonlinear Schrödinger equation in the exterior of a convex obstacle.
arXiv:2012.13335

- O. Landoulsi, S. Roudenko and Kai Yang. Soliton-obstacle interaction in the 2d focusing
NLS equation: Numerical study. (preprint)