Most of my publications can be found on my arxiv page, a comprehensive list follows.
Selected publications
5) Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrodinger equation, with Tristan Buckmaster, Zaher Hani, and Jalal Shatah, Invent. Math. 225 (2021), 787--855.
4) Long wave limit for Schroedinger maps, with Frederic Rousset, J. Eur. Math. Soc. 21 (2019), no. 8, 2517–2602.
3) The weakly nonlinear large box limit of the 2D cubic nonlinear Schrodinger equation, with Erwan Faou and Zaher Hani, J. Amer. Math. Soc. 29 (2016), no. 4, 915--982.
2) On the stability threshold for the 3D Couette flow in Sobolev regularity, with Jacob Bedrossian and Nader Masmoudi, Ann. of Math. (2) 185 (2017), 541--608.
1) Global solutions for the gravity water waves equation in dimension 3, with Nader Masmoudi and Jalal Shatah, Ann. of Math. (2) 175 (2012), 691--75
Survey articles
4) L2 to Lp bounds for spectral projectors on thin intervals in Riemannian manifolds, arXiv preprint.
3) Stability of the Couette flow at high Reynolds number in 2D and 3D, with Jacob Bedrossian and Nader Masmoudi, Bull. Amer. Math. Soc. 56 (2019), no. 3, 373–414.
2) From dispersion management to continuous resonant equations, Proceedings of the ICMP 2015.
1) Space-time resonances, Exp. No 8, Proceedings of the Journees EDP 2010.
All publications
74) On the stability of the Abrikosov lattice in the lowest Landau level, with Valentin Schwinte et Laurent Thomann, arXiv preprint.
73) On universality for the kinetic wave equation, with Hui Zhu, arXiv preprint.
72) Local well-posedness for the kinetic MMT model, with Joonhyun La, arXiv preprint.
71) Standing and traveling waves in a nonlinearly dispersive lattice model, with Ross Parker, Jesus Cuevas-Maraver, Alejandro Aceves and Panos Kevrekidis, accepted by Physica D.
70) L2 to Lp bounds for spectral projectors on the Euclidean two-dimensional torus, with Ciprian Demeter, Proc. Edinb. Math. Soc. 67 (2024), 431--459.
69) Spectral projectors on hyperbolic surfaces, with Jean-Philippe Anker and Tristan Leger, arXiv preprint.
68) Asymptotic stability of solitary waves for one-dimensional nonlinear Schroedinger equations, with Charles Collot, arXiv preprint.
67) Stability and cascades for the Kolmogorov-Zakharov spectrum of wave turbulence, with Charles Collot and Helge Dietert, Arch. Ration. Mech. Anal. 248 (2024), 7.
66) Bounds for spectral projectors on generic tori, with Simon Myerson, Math. Ann. (2022), 1--37.
65) On 1d quadratic Klein–Gordon equations with a potential and symmetries, with Fabio Pusateri and Katherine Zhang, Arch. Ration. Mech. Anal. 247 (2023), 17.
64) Bounds for spectral projectors on the Euclidean cylinder, with Simon Myerson, Comptes Rendus Math. 360 (2022), 1257--1262.
63) Stratospheric planetary flows from the perspective of the Euler equation on a rotating sphere, with Adrian Constantin, Arch. Ration. Mech. Anal. 245 (2022), no. 1, 587--644.
62) Bounds for spectral projectors on tori, with Simon Myerson, Forum Math. Sigma. 10 (2022)
61) Spectral projectors, resolvent, and Fourier restriction on the hyperbolic space, with Tristan Leger, J. Funct. Anal. 285 (2023), no.2, 109918.
60) On the derivation of the kinetic wave equation for a random matrix model, with Guillaume Dubach and Benjamin Harrop-Griffiths, Ars Inveniendi Analytica (2023).
59) Quadratic Klein-Gordon equations with a potential in one dimension, with Fabio Pusateri, Forum Math., Pi. 10 (2022).
58) Derivation of the kinetic wave equation for quadratic dispersive problems in the inhomogeneous setting, with Ioakeim Ampatzoglou and Charles Collot, accepted by Am. J. Math.
57) Derivation of the homogeneous kinetic wave equation: longer time scales, with Charles Collot, arXiv preprint.
56) On the derivation of the homogeneous kinetic wave equation, with Charles Collot, accepted by Comm. Pure Appl. Math.
55) On self-similar solutions to degenerate compressible Navier-Stokes equations, with Tsukasa Iwabuchi and Tristan Leger, Comm. Math. Phys. 381 (2021), no. 3, 1001--1030
54) Backward self-similar solutions for compressible Navier-Stokes equations, with Tsukasa Iwabuchi and Tristan Leger, Nonlinearity 34 (2021), no. 2, 868--893.
53) Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrodinger equation, with Tristan Buckmaster, Zaher Hani, and Jalal Shatah, Invent. Math. 225 (2021), 787--855.
52) Self-similar solutions for compressible Navier-Stokes equations, with Tsukasa Iwabuchi, Arch. Ration. Mech. Anal. 240 (2021), no. 3, 1645--1673
51) Strichartz estimates for the Schroedinger equation on non-rectangular two-dimensional tori, with Yu Deng, Larry Guth and Simon Meyerson, Am. J. Math. 144 (2022), no. 3, 701--745.
50) Vortex filament solutions of the Navier-Stokes equations, with Jacob Bedrossian and Benjamin Harrop-Griffiths, Comm. Pure Appl. Math. 76 (2023), no. 4, 685--787.
49) Optimal local well-posedness theory for the kinetic wave equation, with Alexandru Ionescu and Minh-Binh Tran, J. Funct. Anal. 279 (2020), no. 4, 108570
48) Existence and uniqueness of solutions for a quasilinear KdV equation with degenerate dispersion, with Benjamin Harrop-Griffiths and Jeremy Marzuola, Comm. Pure Appl. Math. 72 (2019), no. 11, 2449--2484.
47) Compactons and their variational properties for degenerate KdV and NLS in dimension 1, with Benjamin Harrop-Griffiths and Jeremy Marzuola, Quart. Appl. Math. 78 (2020), no. 1, 1--32.
46) On the Cubic Lowest Landau Level Equation, with Patrick Gerard and Laurent Thomann, Arch. Ration. Mech. Anal. 231 (2019), no. 2, 1073--1128.
45) The nonlinear Schrodinger equation with a potential in dimension 1, with Fabio Pusateri and Frederic Rousset, Ann. Inst. H. Poincare Anal. Non Lineaire 35 (2018), no. 6, 1477--1530.
44) Growth of solutions of NLS on irrational tori, with Yu Deng, Int. Math. Res. Not. IMRN 2019, no. 9, 2919--2950.
43) Strichartz estimates for the Schrodinger equation on irrational tori, with Yu Deng and Larry Guth, J. Funct. Anal. 273 (2017), no. 9, 2846--2869.
42) Analysis of the (CR) equation in higher dimensions, with Tristan Buckmaster, Zaher Hani, and Jalal Shatah.
41) Effective dynamics of the nonlinear Schrodinger equation on large domains, with Tristan Buckmaster, Zaher Hani, and Jalal Shatah, Comm. Pure Appl. Math. 71 (2018), no. 7, 1407–1460.
40) Long wave limit for Schroedinger maps, with Frederic Rousset, J. Eur. Math. Soc. 21 (2019), no. 8, 2517–2602.
39) On uniqueness for the Harmonic Map Heat Flow in supercritical dimension, with Tej-Eddine Ghoul and Hideyuki Miura. Comm. Pure Appl. Math. 70 (2017), no. 12, 2247–2299.
38) On the high frequency limit of the LLL equation, with Laurent Thomann, Quart. Appl. Math. 74 (2016), no. 4, 633–641.
37) On the stability threshold for the 3D Couette flow in Sobolev regularity, with Jacob Bedrossian and Nader Masmoudi, Ann. of Math. (2) 185 (2017), no. 2, 541–608.
36) Dynamics near the subcritical transition of the 3D Couette flow II: Above threshold case, with Jacob Bedrossian and Nader Masmoudi.
35) Dynamics near the subcritical transition of the 3D Couette flow I: Below threshold case, with Jacob Bedrossian and Nader Masmoudi, Mem. Amer. Math. Soc. 266 (2020), no. 1294
34) Asymptotic stability of solitons for mKdV, with Fabio Pusateri and Frederic Rousset, Adv. Math. 299 (2016), 272–330.
33) On the continuous resonant equation for NLS: II. Statistical study, with Laurent Thomann and Zaher Hani, Anal. PDE 8 (2015), no. 7, 1733–1756.
32) On the continuous resonant equation for NLS: I. Deterministic analysis, with Laurent Thomann and Zaher Hani, J. Math. Pures Appl. (9) 105 (2016), no. 1, 131–163.
31) An extension of the Derrida-Lebowitz-Speer-Spohn equation, with Charles Bordenave, J. Phys. A 48 (2015), no. 48, 485205
30) Bilinear dispersive estimates via space-time resonances, part II: dimensions 2 and 3, with Frederic Bernicot, Arch. Ration. Mech. Anal. 214 (2014), no. 2, 617–669.
29) The weakly nonlinear large box limit of the 2D cubic nonlinear Schrodinger equation, with Erwan Faou and Zaher Hani, J. Amer. Math. Soc. 29 (2016), no. 4, 915--982.
28) Nonlinear resonances with a potential: multilinear estimates and an application to NLS, with Zaher Hani and Sam Walsh, Int. Math. Res. Not. IMRN 2015, no. 18, 8484--8544.
27) Instability of some equatorially trapped waves, with Adrian Constantin.
26) The finite energy method for compressible fluids. The Navier-Stokes-Korteweg model, with Philippe LeFloch, Comm. Pure Appl. Math. 69 (2016), no. 1, 3--61.
25) Global existence for capillary water-waves, with Nader Masmoudi and Jalal Shatah, Comm. Pure Appl. Math. 68 (2015), no. 4, 625--687.
24) Well-posedness of the Navier-Stokes-Maxwell equations, with Slim Ibrahim and Nader Masmoudi, Proc. Roy. Soc. Edinburgh Sect. A 144 (2014), no. 1, 71--86.
23) 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.
22) Bilinear dispersive estimates via space time resonances. Part I: the one-dimensional case, with Frederic Bernicot, Anal. PDE 6 (2013), no. 3, 687--722.
21) 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.
20) Global existence for the Euler-Maxwell system, with Nader Masmoudi, Ann. Sci. Ec. Norm. Super. (4) 47 (2014), no. 3, 469--503.
19) Boundedness of bilinear multipliers whose symbols have a narrow support, with Frederic Bernicot, J. Anal. Math. 119 (2013), 166--212.
18) Self-similar expanders of the harmonic map flow, with Melanie Rupflin, Ann. Inst. H. Poincare Anal. Non Lineaire 28 (2011), no. 5, 743--773.
17) Global solutions for coupled Klein-Gordon equations with different speeds, Ann. Inst. Fourier (Grenoble) 61 (2011), no. 6, 2463--2506.
16) Global solutions for 2D quadratic Schroedinger equations, with Nader Masmoudi and Jalal Shatah, J. Math. Pures Appl. (9) 97 (2012), no. 5, 505--543.
15) 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.
14) 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.
13) Bilinear oscillatory integrals and boundedness for new bilinear multipliers, with Frederic Bernicot, Adv. Math. 225 (2010), no. 4, 1739--1785.
12) Weak-strong uniqueness for the isentropic compressible Navier-Stokes system, J. Math. Fluid Mech. 13 (2011), no. 1, 137--146.
11) Self-similar solutions for the Schroedinger map equation, with Jalal Shatah and Chongchun Zeng, Math. Z. 264 (2010), no. 3, 697--707.
10) Global solutions for 3D quadratic Schroedinger equations, with Nader Masmoudi and Jalal Shatah, Int. Math. Res. Not. IMRN 2009, no. 3, 414--432.
9) 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.
8) The second iterate for the Navier-Stokes equation, J. Funct. Anal. 255 (2008), no. 9, 2248--2264.
7) Besov spaces and self-similar solutions for the wave-map equation, Comm. Partial Differential Equations 33 (2008), no. 7-9, 1571--1596.
6) Strong solutions and weak-strong uniqueness for the nonhomogeneous Navier-Stokes equation, J. Anal. Math. 105 (2008), 169--196.
5) Global infinite energy solutions of the critical semilinear wave equation, Rev. Mat. Iberoam. 24 (2008), no. 2, 463--497.
4) Finite energy scattering for the Lorentz-Maxwell equation, Ann. Henri Poincare 9 (2008), no. 5, 927--943.
3) 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.
2) Multipliers, Paramultipliers, and weak-strong uniqueness for the Navier-Stokes equations, J. Differential Equations 226 (2006), no. 2, 373--428.
1) Equations de Navier-Stokes en deux dimensions : existence et comportement asymptotique de solutions d'energie infinie, Bull. Sci. Math. 130 (2006), no. 2, 123--151.