Thomas Alazard

FMJH (Fondation mathématiques Jacques Hadamard)

I am in charge of the Sophie Germain master's scholarships.

École Polytechnique

Vice President of the Department.

Co-organizer of the Laurent Schwartz Seminar.

Editorial Work

Editor at Forum Mathematicum.

Analyse et Équations aux Dérivées Partielles

EDP Sciences, Les Ulis; CNRS Éditions, Paris, 2023, viii+436 pp.

Analysis and Partial Differential Equations

Universitext, Springer, Cham, 2024, xiv+439 pp.

Tools and Problems in Partial Differential Equations (with Claude Zuily)

Universitext Springer, Cham, 2020, xii+357 pp.

Free Boundary Problems in Fluid Dynamics (with Albert Ai, Mihaela Ifrim and Daniel Tataru)

Oberwolfach Semin., 54, Birkhauser/Springer, Cham, 2024, xiv+362 pp.

Paralinearization of free boundary problems in fluid dynamics

Published in Partial Differential Equations: Waves, Nonlinearities and Nonlocalities, The Abel Symposium 2023.

Introduction to microlocal analysis

Lecture Notes for a course at Tsinghua University in Summer 2021

Free surface flows in fluid dynamics

Lecture Notes for a course at UC Berkeley in Spring 2021

A minicourse on the low Mach number limit

Discrete Contin. Dyn. Syst. Ser. S 1 (2008), no. 3, 365-404.

Generic small-scale creation in the two-dimensional Euler equation (with Ayman Rimah Said)

arXiv:2603.13079

Global well-posedness of a 2D fluid-structure interaction problem with free surface (with Chengyang Shao and Haocheng Yang)

arXiv:2504.00213

Paracomposition Operators and Paradifferential Reducibility (with Chengyang Shao)

arXiv:2410.17211

Nonlinear interpolation and the flow map for quasilinear equations (with Nicolas Burq, Mihaela Ifrim, Daniel Tataru, Claude Zuily)

J. Eur. Math. Soc., to appear. arXiv:2410.06909

Global-in-time weak solutions for an inviscid free surface fluid-structure problem without damping (with Igor Kukavica and Amjad Tuffaha)

Annals of PDE, 11, No. 1, Paper No. 15, 40 p. (2025).

KAM via Standard Fixed Point Theorems (with Chengyang Shao)

Forum Math. Sigma, to appear. arXiv:2312.13971.

The Hele-Shaw semi-flow (with Herbert Koch)

arXiv:2312.13678.

Damping for fractional wave equations and applications to water waves (with Jeremy L. Marzuola and Jian Wang)

J. Math. Pures Appl. (9) 196 (2025), Article ID 103692, 33 p.

Virial theorems and equipartition of energy for water-waves (with Claude Zuily)

SIAM J. Math. Anal., 56 (2024), no. 4, 5285-5329.

Refined Rellich boundary inequalities for the derivatives of a harmonic function (with Siddhant Agrawal)

Proc. Amer. Math. Soc. 151 (2023), no. 5, 2103-2113.

Traveling wave solution for a coupled incompressible Darcy's free boundary problem with surface tension (with Martina Magliocca and Nicolas Meunier)

On the dynamics of the roots of polynomials under differentiation (with Omar Lazar and Quoc-Hung Nguyen)

J. Math. Pures Appl. (9) 162 (2022), 1-22.

Quasilinearization of the 3D Muskat equation, and applications to the critical Cauchy problem (with Quoc-Hung Nguyen)

Adv. Math. 399 (2022), Paper No. 108278, 52 pp.

Endpoint Sobolev theory for the Muskat equation (with Quoc-Hung Nguyen)

Commun. Math. Phys. 397 (2023), no. 3, 1043-1102.

On the Cauchy problem for the Muskat equation. II: Critical initial data (with Quoc-Hung Nguyen)

Annals of PDE 7 (2021), no. 1, Paper No. 7, 25pp.

On the Cauchy problem for the Muskat equation with non-Lipschitz initial data (with Quoc-Hung Nguyen)

Comm. Partial Differential Equations 46, no. 11, 2171-2212 (2021).

Cauchy theory for the water waves system in an analytic framework (with Nicolas Burq and Claude Zuily)

Tokyo J. Math., 45(1), 103-199 (2022).

Functional inequalities and strong Lyapunov functionals for free surface flows in fluid dynamics (with Didier Bresch)

Interfaces Free Bound. 26(1), 1-30 (2024). (Note: the arXiv version contains more results than the published version.)

Convexity and the Hele-Shaw equation

Water Waves 3 (2021), no. 1, 5-23.

A Morawetz inequality for gravity-capillary water waves at low Bond number (with Mihaela Ifrim and Daniel Tataru)

Water Waves 3 (2021), no. 3, 429-472.

Lyapunov functions, Identities and the Cauchy problem for the Hele-Shaw equation (with Nicolas Meunier and Didier Smets)

Commun. Math. Phys. 377 (2020), no. 2, 1421-1459.

Paralinearization of the Muskat equation and application to the Cauchy problem (with Omar Lazar)

Arch. Ration. Mech. Anal., 237 (2020), no. 2, 545-583.

A Morawetz inequality for water waves (with Mihaela Ifrim and Daniel Tataru)

Amer. J. Math., 144 (2022), no. 3, 607-699.

Stabilization of the water-wave equations with surface tension

Annals of PDE (2017), no. 2, Art. 17, 41 pp.

Stabilization of gravity water waves

J. Math. Pures Appl. (9) 114 (2018), 51-84.

A stationary phase type estimate (with Nicolas Burq and Claude Zuily)

Proc. Amer. Math. Soc., 145 (2017), 2871-2880.

Boundary observability of gravity water waves

Ann. Inst. H. Poincaré Anal. Non Linéaire, 35 (2018), no. 3, 751-779.

Control for water waves (with Pietro Baldi and Daniel Han-Kwan)

J. Eur. Math. Soc., 20 (2018) 657-745.

Gravity capillary standing water waves (with Pietro Baldi)

Arch. Ration. Mech. Anal., 217 (2015), no 3, 741-830.

Strichartz estimates and the Cauchy problem for the gravity water waves equations (with Nicolas Burq and Claude Zuily)

Memoirs of the AMS, 2018; Volume 256, 115pp.

Global solutions and asymptotic behavior for two dimensional gravity water waves (with Jean-Marc Delort)

Ann. Sci. Éc. Norm. Supér., 48, (2015), no. 5, 1149-1238.

Sobolev estimates for two dimensional gravity water waves (with Jean-Marc Delort)

Astérisque 374 (2015), viii+241 pages.

Cauchy theory for the gravity water waves system with non localized initial data (with Nicolas Burq and Claude Zuily)

Ann. Inst. H. Poincaré Anal. Non Linéaire, 33 (2016), 337-395.

The water-waves equations: from Zakharov to Euler (with Nicolas Burq and Claude Zuily)

Studies in Phase Space Analysis with Applications to PDEs. Progress in Nonlinear Differential Equations and Their Applications Volume 84, 2013, pp 1-20.

On the Cauchy problem for gravity water waves (with Nicolas Burq and Claude Zuily)

Invent. Math., 198 (2014), 71-163.

Strichartz estimates for water waves (with Nicolas Burq and Claude Zuily)

Ann. Sci. Éc. Norm. Supér. (4), 44 (2011), no. 5, 855-903.

On the water waves equations with surface tension (with Nicolas Burq and Claude Zuily)

Duke Math. J., 158 (2011), no. 3, 413-499.

Paralinearization of the Dirichlet to Neumann operator, and regularity of diamond waves (with Guy Métivier)

Comm. Partial Differential Equations, 34 (2009), no. 10-12, 1632-1704.

Semi-classical limit of Schrödinger-Poisson equations in space dimension n≥3 (with Rémi Carles)

J. Differential Equations, 233 (2007), no. 1, 241-275.

Loss of regularity for super-critical nonlinear Schrödinger equations (with Rémi Carles)

Math. Ann., 343 (2009), no. 2, 397-420.

Super critical geometric optics for nonlinear Schrödinger equations (with Rémi Carles)

Arch. Ration. Mech. Anal. 194 (2009), no. 1, 315-347.

WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity (with Rémi Carles)

Ann. Inst. H. Poincaré Anal. Non Linéaire, 26 (2009), no. 3, 959-977.

Low Mach number flows and combustion

SIAM J. Math. Anal. 38 (2006), no. 4, 1186-1213.

Low Mach number limit of the full Navier-Stokes equations

Arch. Ration. Mech. Anal. 180 (2006), no. 1, 1-73.

Incompressible limit of the nonisentropic Euler equations with the solid wall boundary conditions

Adv. Differential Equations 10 (2005), no. 1, 19-44.

Controllability and Stabilization of water waves

Séminaire Laurent Schwartz. Année 2015-2016, Exp. No. VII, 17 pp.

About global existence and asymptotic behavior for two dimensional gravity water waves

Séminaire Laurent Schwartz - EDP et applications (2012-2013), Exp. No. 18, 16 p.

Low regularity theory for the water-waves problem: canals and swimming pools (with Nicolas Burq and Claude Zuily)

Journées Équations aux Dérivées Partielles, Biarritz 2011.

On the Cauchy problem and the Kato smoothing effect for water waves (with Nicolas Burq and Claude Zuily)

Harmonic analysis and nonlinear partial differential equations, 1-14, RIMS Kôkyûroku Bessatsu, B18, Kyoto, 2010.

Les travaux de Iooss et Plotnikov sur les vagues tri-dimensionnelles

Gazette Société Mathématique de France No. 126 (2010), 24-45.