Papers and preprints

Articles:
[1] Scattering and the Levandosky-Strauss conjecture for fourth order nonlinear wave equations,
J. Differential Equations, 241 (2), (2007), 237-278.
[2] Global well-posedness for energy critical fourth-order Schrödinger equations in the radial case,
Dynamics of PDE, 4 (3), (2007), 197-225.
[3] The focusing energy-critical fourth-order Schrödinger equation with radial data,
DCDS-A, 24 (2009), 4, 1275-1292.
[4] The cubic fourth-order Schrödinger equation,
J. Funct. Anal., 256 (2009), 8, 2473-2517, arXiv.
[5] Analyticity of the nonlinear scattering operator, (with W.A. Strauss),
Discrete Contin. Dyn. Syst. 25 (2009), no. 2, 617-626.
[6] Scattering for the Beam equation in low dimensions,
Indiana Univ. Math. J., 59 (2010), no. 3, 791-822, arXiv.
[7] The mass-critical fourth-order Schrödinger equation in high dimensions, (with S. Shao),
J. Hyp. Diff. Equ, 7 (2010), no. 4, 651-705, arXiv.
[8] The linear profile decomposition for the fourth order Schrödinger equation, (with J.C. Jiang and S. Shao)
J. Differential Equations 249 (2010) 2521-2547, arXiv.
[9] Global Smooth Ion Dynamics in the Euler-Poisson System, (with Y. Guo),
Comm. Math. Phys. 303 (2011), 89-125, arXiv.
[10] On the global well-posedness of energy-critical Schrödinger equations in curved spaces, (with A. Ionescu and G. Staffilani),
Analysis and PDE, Vol. 5 (2012), no. 4, 705-746, arXiv.
[11] Global well-posedness of the energy-critical defocusing NLS on RxT^3, (with A. Ionescu),
Comm. Math. Phys., 312 (2012), no. 3, 781-831, arXiv.
[12] The energy-critical defocusing NLS on T^3, (with A. Ionescu),
Duke Math. J., 161 (2012), no. 8, 1581-1612, arXiv.
[13] The Euler-Poisson system in 2D: global stability of the constant equilibrium solution (with A. Ionescu),
Int. Math. Res. Not., 2013 (2013), 761-826, arXiv.
[14] Non-neutral global solutions for the electron Euler-Poisson system in 3D (with P. Germain and N. Masmoudi),
SIMA, 45-1 (2013), 267-278, arXiv.
[15] Dynamics of particle settling and resuspension in viscous liquids (with N. Murisic, D. Peschka and A.L. Bertozzi),
J. Fluid. Mech., 717 (2013), 203-231.
[16] On scattering for the quintic defocusing nonlinear Schrödinger equation on RxT^2 (with Z. Hani),
CPAM, 67 (2014), no. 9, 1466-1542, arXiv.
[17] Global solutions of quasilinear systems of Klein-Gordon equations in 3D (with A. Ionescu),
JEMS, 16, (2014), no. 11, 2355-2431, arXiv.
[18] Global regularity for the energy-critical NLS on S^3 (with N. Tzvetkov and X. Wang),
Ann. I.H.P., Analyse non lin., 31 (2014), no. 2, 315-338, arXiv.
[19] Scattering Theory for the fourth-order Schrödinger equation in low dimensions (with S. Xia),
Nonlinearity, 26 (2013), no. 8, 2175-2191.
[20] Topography influence on the lake equation in bounded domains (with C. Lacave and T. N'Guyen),
J. Math. Fluid. Mech., 16 (2014), no. 2, 375-406, arXiv.
[21] Global solutions of certain plasma fluid models in 3D (with Y. Guo and A. Ionescu),
J. Math. Phys. 55, 123102 (2014).
[22] Modified scattering for the cubic nonlinear Schrödinger equation on product space and applications (with Z. Hani, N. Tzvetkov and N. Visciglia), Forum of Mathematics, Pi, Vol. 3 / 2015, e4, arXiv.
[23] Global solutions of the Euler-Maxwell two-fluid system in 3D (with Y. Guo and A. Ionescu), Ann. of Math. (2) 183 (2016), no. 2, 377-498, arXiv.
[24] Discrete Schrödinger equation and ill-posedness for the Euler equation (with I.J. Jeong), Discrete Contin. Dyn. Syst. 37 (2017), no. 1, 281-293, paper.
[25] The Euler-Maxwell system for electrons: global solutions in 2D (with Y. Deng and A. Ionescu), ARMA, to appear, arXiv.

Preprints:
[26] Global solutions of the capillary-gravity water wave system in 3 dimensions (with Y. Deng, A. Ionescu and F. Pusateri), arXiv. [27] On the global regularity for a Wave-Klein-Gordon coupled system (with A. Ionescu), arXiv

Here, you can download my PhD dissertation.

Expository texts:
[1] An introduction to fourth order nonlinear wave equations, with E. Hebey,
FourthOrderWaves.pdf , 48 pages, 2008. Unpublished.
[2] Scattering for the Beam equation, Proceedings of GDR "équations aux dérivées partielles", Evian, 2008.