Finite time singularity formation and asymptotic stability
Standing ring blow up solutions to the N-dimensional quintic nonlinear Schrödinger equation (with P. Raphaël)
Comm. Math. Phys. 290 (3), 973-996, 2009.
Stable self similar blow up dynamics for slightly L2 supercritical NLS equations (with F. Merle and P. Raphaël)
Geom. Funct. Anal. 20 (4), 1028-1071, 2010.
Existence and uniqueness of minimal blow up solutions
to an inhomogeneous mass critical NLS (with P. Raphaël)
J. Amer. Math. Soc. 24, 471-546, 2011.
The instability of Bourgain-Wang solutions for the L2 critical NLS (with F. Merle and P. Raphaël)
Amer. J. Math. 135 (4), 967-1017, 2013.
On collapsing ring blow up solutions to
the mass supercritical NLS (with F. Merle and P. Raphaël)
Duke Math. J. 163 (2), 369-431, 2014.
Codimension one stability of the
catenoid under the vanishing mean curvature flow in Minkowski space
(with R. Donninger, J. Krieger and W. Wong)
Math. J. 165 (4), 723-791, 2016.
On the stability of type I blow up for
the energy super critical heat equation (with C. Collot and
Mem. Amer. Math. Soc. 260, no 1255, v+97 pp., 2019.
On strongly anisotropic type I
blow up (with F. Merle and P. Raphaël)
Int. Math. Res. Not., 541-606, 2020.
On smooth self similar solutions to the compressible Euler equations (with F. Merle, P. Raphaël and I. Rodnianski)
On blow up for the energy super critical defocusing non linear Schröodinger equations (with F. Merle, P. Raphaël and I. Rodnianski)
On the implosion of a three dimensional compressible fluid (with F. Merle, P. Raphaël and I. Rodnianski)
Derivation of the nonlinear Schrödinger equation
Domain decomposition methods
Long-time existence problems on compact manifolds
Absorbing boundary conditions
Absorbing boundary conditions for reaction diffusion equation.
IMA J. Appl. Math. 68 (2), 167-184, 2003.
Design of absorbing boundary conditions for Schrödinger equations in Rd.
SIAM J. Numer. Anal. 42 (4), 1527-1551, 2004.
A nonlinear approach to absorbing boundary conditions for the semilinear wave equation.
Math. Comp.75, 565-594, 2006.
Absorbing boundary conditions for nonlinear scalar partial differential equations
Comput. Methods Appl. Mech. Engrg. 195, 3760-3775, 2006.
Absorbing boundary conditions for nonlinear Schrödinger equations
Numerische Mathematik 104, 103-127, 2006.
Towards accurate artificial boundary conditions for nonlinear PDEs through examples (with X. Antoine and C. Besse)
Cubo, 11 (4), 29-48, 2009.
Propagation/ reflection of singularities, smoothing effect
I defended my Habilitation thesis on October 8th 2012 (Univerité Paris 13).
You can download my Habilitation thesis in .pdf.
Between October 2000 and April 2004, I have been doing a PhD on
"Pseudodifferential and paradifferential calculus for the study of
absorbing boundary conditions and qualitative properties of nonlinear
PDE's" at Univerité Paris 13 under the guidance of Laurence Halpern.
You can download my PhD thesis in .pdf.
Here is the proceeding of the talk I gave at ICM 2014 The resolution of the bounded
L2 curvature conjecture in general relativity.