Papers

• The Bounded L² Curvature Conjecture (with S. Klainerman and I. Rodnianski)
  Invent. Math. 202 (1), 91-216, 2015.


• Sharp Strichartz estimates for the wave equation on a rough background
  Annales Scientifiques de l'Ecole Normale Supérieure 49 (6), 1279-1309, 2016.


• Global regularity for the 2+1 dimensional equivariant Einstein-wave map system (with L. Andersson and N. Gudapati)
  Ann. PDE 3 (2), Art. 13, 142 pp., 2017.


• Parametrix for wave equations on a rough background III: space-time regularity of the phase
  Astérisque 401, 321 pp., 2018.


• Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations (with S. Klainerman)
  Annals of Math Studies, 210. Princeton University Press, Princeton, NJ, 2020, xviii+856 pp.


• Constructions of GCM spheres in perturbations of Kerr (with S. Klainerman)
  Ann. PDE 8 (2), Art. 17, 153 pp., 2022.


• Effective results on uniformization and intrinsic GCM spheres in perturbations of Kerr (with S. Klainerman)
  Ann. PDE 8 (2), Art. 18, 89 pp., 2022.


• Kerr stability for small angular momentum (with S. Klainerman)
  Pure and Applied Mathematics Quarterly 19 (3), 791-1678, 2023.


• Parametrix for wave equations on a rough background I: regularity of the phase at initial time
  Accepted for publication in Astérisque.


• Parametrix for wave equations on a rough background II: construction and control at initial time
  Accepted for publication in Astérisque.


• Parametrix for wave equations on a rough background IV: control of the error term
  Accepted for publication in Astérisque.


• Wave equations estimates and the nonlinear stability of slowly rotating Kerr black holes (with E. Giorgi and S. Klainerman)
  Submitted.

• 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)
  Duke 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 P. Raphaël)
  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 blow up for the energy super critical defocusing non linear Schröodinger equations (with F. Merle, P. Raphaël and I. Rodnianski)
  Invent. Math., 227 (1), 247-413, 2022.


• On the implosion of a compressible fluid I: Smooth self-similar inviscid profiles (with F. Merle, P. Raphaël and I. Rodnianski)
  Annals of Math., 196 (2), 567-778, 2022.


• On the implosion of a compressible fluid II: Singularity formation (with F. Merle, P. Raphaël and I. Rodnianski)
  Annals of Math., 196 (2), 779-889, 2022.

• Variants of the focusing NLS equation. Derivation, justification and open problems related to filamentation (with E. Dumas and D. Lannes)
  Laser Filamentation, CRM Series in Mathematical Physics, pages 19-75. Springer International Publishing, 2016.

• Nonlinear Nonoverlapping Schwarz Waveform Relaxation for Semilinear Wave Propagation (with L. Halpern)
  Math. Comp. 78, 865-889, 2009.


• Schwarz waveform relaxation algorithms for semilinear reaction-diffusion equations (with F. Caetano, M. Gander and L. Halpern)
  Netw. Heterog. Media 5 (3), 487-505, 2010.


• Optimized and Quasi-Optimal Schwarz Waveform Relaxation for the One Dimensional Schrödinger equation (with L. Halpern)
  Math. Models Methods Appl. Sci. 20 (12), 2167-2199, 2010.


• Optimized Schwarz waveform relaxation and discontinuous Galerkin time stepping for heterogeneous problems (with C. Japhet and L. Halpern)
  SIAM J. Numer. Anal. 50 (5), 2588-2611, 2012.

• Long time existence for small data nonlinear Klein-Gordon equations on tori and spheres (with J. M. Delort).
  Int. Math. Res. Not. 37, 1897-1966, 2004.


• Long-time existence for semi-linear Klein-Gordon equations with small Cauchy data on Zoll manifolds (with J. M. Delort)
  Amer. J. Math. 128, 1187-1218, 2006.


• Bounded almost global solutions for non hamiltonian semi-linear Klein-Gordon equations with radial data on compact revolution hypersurfaces (with J. M. Delort)
  Ann. Inst. Fourier (Grenoble) 56, 1419-1456, 2006.


• Almost global existence for Hamiltonian semi-linear Klein-Gordon equations with small Cauchy data on Zoll manifolds (with D. Bambusi, J. M. Delort and B. Grébert)
  Comm. Pure. Appl. Math. 60, 1665-1690, 2007.

• 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 R^d.
  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.

• Réflexion des singularités pour Schrödinger.
  Comm. Partial Differential Equations 29 (5-6), 707-761, 2004.


• Propagation et réflexion des singularités pour l'équation de Schrödinger non linéaire
  Ann. Inst. Fourier (Grenoble) 55 (2), 573-671, 2005.


• Microlocal smoothing effect for the nonlinear Schrödinger equation.
  SIAM J. Math. Anal. 37 (2), 549-597, 2005.