Courant Institute of Mathematical
New York University
251 Mercer Street
New York, N.Y. 10012-1185
TEACHING: In the Spring 2015 Semester, I am teaching PDE2. Below are lecture notes and Homework:
Notes 1. HW1.
Notes 2. HW2.
Notes 3. HW3.
Notes 4. HW4.
Research domains: fluid mechanics, nonlinear wave equations, harmonic analysis.
Here is my CV.
I defended in 2005 my PhD, which I had prepared under the supervision of Isabelle Gallagher; I defended in 2008 my "Habilitation a diriger des recherches".
Since January 2015, I am an Associate Professor at the Courant Institute.
I am an editor for DCDS-A
Current PhD students
Nicolas Laillet (jointly with Isabelle Gallagher)
- Equations de Navier-Stokes
en deux dimensions : existence et comportement asymptotique de
solutions d'energie infinie, Bull. Sci. Math. 130 (2006), no.
- Multipliers, Paramultipliers, and
weak-strong uniqueness for the Navier-Stokes equations, J.
Differential Equations 226 (2006), no. 2, 373--428
- Regularity of solutions to the
Navier-Stokes equations evolving from small data in BMO-1
, with Natasa Pavlovic and Gigliola Staffilani, Int. Math. Res. Not. IMRN 2007, no. 21.
energy scattering for the Lorentz-Maxwell equation, Ann. Henri Poincare 9 (2008), no. 5, 927--943.
- Global infinite energy solutions
of the critical semilinear wave equation, Rev. Mat. Iberoam. 24 (2008), no. 2, 463--497.
- Strong solutions and weak-strong
uniqueness for the nonhomogeneous Navier-Stokes equation, J. Anal. Math. 105 (2008), 169--196.
- Besov spaces and self-similar solutions for the wave-map
equation., Comm. Partial Differential Equations 33 (2008), no. 7-9, 1571--1596.
- The second
iterate for the Navier-Stokes equation, J. Funct. Anal. 255 (2008), no. 9, 2248--2264.
- On the existence of smooth self-similar blow up profiles for the
wave map equation, Comm. Pure Appl. Math. 62 (2009), no. 5, 706--728.
solutions for 3D quadratic Schroedinger equations, with Nader
Masmoudi and Jalal Shatah, Int. Math. Res. Not. IMRN 2009, no. 3, 414--432.
- Self-similar solutions for the Schroedinger map equation, with
Jalal Shatah and Chongchun Zeng, Math. Z. 264 (2010), no. 3, 697--707.
- Weak-strong uniqueness for the isentropic compressible Navier-Stokes
system, J. Math. Fluid Mech. 13 (2011), no. 1, 137--146.
Bilinear oscillatory integrals and boundedness for new bilinear multipliers, with Frederic Bernicot, Adv. Math. 225 (2010), no. 4, 1739--1785.
- Global solutions
for the gravity water waves equation in dimension 3 (note announcing the result),
with Nader Masmoudi and Jalal Shatah, C. R. Math. Acad. Sci. Paris 347 (2009), no. 15-16, 897--902.
- Global solutions
for the gravity water waves equation in dimension 3 (full article),
with Nader Masmoudi and Jalal Shatah, Ann. of Math. (2) 175 (2012), no. 2, 691--754.
Global solutions for 2D quadratic Schroedinger equations, with Nader Masmoudi and Jalal Shatah, J. Math. Pures Appl. (9) 97 (2012), no. 5, 505--543.
Global solutions for coupled Klein-Gordon equations with different speeds, Ann. Inst. Fourier (Grenoble) 61 (2011), no. 6, 2463--2506.
Space-time resonances, Exp. No 8, Proceedings of the Journees EDP 2010.
- Self-similar expanders of the harmonic map flow, with Melanie Rupflin, Ann. Inst. H. Poincare Anal. Non Lineaire 28 (2011), no. 5, 743--773.
- Boundedness of bilinear multipliers whose symbols have a narrow support, with Frederic Bernicot, J. Anal. Math. 119 (2013), 166--212.
- Global existence for the Euler-Maxwell system, with Nader Masmoudi.
- On the open sea propagation of water waves generated by a moving bed, with Adrian Constantin, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 370 (2012), no. 1964, 1587--1601.
- Bilinear dispersive estimates via space time resonances. Part I: the one-dimensional case, with Frederic Bernicot, Anal. PDE 6 (2013), no. 3, 687-722.
- Non-neutral global solutions for the electron Euler-Poisson system in 3D, with Nader Masmoudi and Benoit Pausader, SIAM J. Math. Anal. 45 (2013), no. 1, 267--278.
- Well-posedness of the Navier-Stokes-Maxwell equations, with Slim Ibrahim and Nader Masmoudi, accepted by the Proceedings of the Royal Society of Edinburgh Section A.
- Global existence for capillary water-waves, with Nader Masmoudi and Jalal Shatah, accepted by Communications in Pure and Applied Mathematics.
- The finite energy method for compressible fluids. The Navier-Stokes-Korteweg model, with Philippe LeFloch.
- Instability of some equatorially trapped waves, with Adrian Constantin.
- Nonlinear resonances with a potential: multilinear estimates and an application to NLS, with Zaher Hani and Sam Walsh.
- The weakly nonlinear large box limit of the 2D cubic nonlinear Schrodinger equation, with Erwan Faou and Zaher Hani.
- Bilinear dispersive estimates via space-time resonances, part II: dimensions 2 and 3 , with Frederic Bernicot.
- An extension of the Derrida-Lebowitz-Speer-Spohn equation, with Charles Bordenave.
- On the continuous resonant equation for NLS: I. Deterministic analysis, with Laurent Thomann and Zaher Hani.
- On the continuous resonant equation for NLS: II. Statistical analysis, with Laurent Thomann and Zaher Hani.