Thematical list of publications

(see here for a chronological list)


Navier-Stokes equations

  1. The tridimensional Navier-Stokes equations with almost bidimensional data: stability, uniqueness and life span , .ps
    International Mathematics Research Notices, 18, pages 919-935, 1997.
  2. A remark on smooth solutions of the weakly compressible Navier-Stokes equations, .ps
    Journal of Mathematics of Kyoto University, 40, pages 525-540, 2000.
  3. Fluids with anisotropic viscosity, .ps
    (with J.-Y. Chemin, B. Desjardins and E. Grenier)
    Modélisation Mathématique et Analyse Numérique, 34, pages 315--335, 2000.
  4. Existence et unicité pour le système de Navier-Stokes axisymétrique, ps and erratum
    (with M. Majdoub and S. Ibrahim)
    Communications in Partial Differential Equations, 26, pages 883-907, 2001.
  5. Profile decomposition for solutions of the Navier-Stokes equations, .ps
    Bulletin de la Société Mathématique de France, 129, pages 285-316, 2001.
  6. Mathematical analysis of a structure-preserving approximation of the bidimensional vorticity equation, .ps
    Numerische Mathematik,91, pages 223-236, 2002.
  7. On global infinite energy solutions to the Navier-Stokes equations in two dimensions, .ps
    (with F. Planchon),
    Archive for Rational Mechanics and Analysis, 161, pages 307-337, 2002.
  8. Stability and weak-strong uniqueness for axisymmetric solutions of the Navier-Stokes equations, .ps
    Differential and Integral Equations, 16, 5, pages 557-572, 2003.
  9. Asymptotics and stability for global solutions to the Navier--Stokes equations, .ps
    (with D. Iftimie and F. Planchon),
    Annales de l'Institut Fourier, 53, 5, pages 1387-1424, 2003.
  10. Uniqueness for the two-dimensional Navier-Stokes equation with a measure as initial vorticity, .ps
    (with Th. Gallay),
    Mathematische Annalen, 332, pages 287-327, 2005.
  11. On the uniqueness of the solution of the two-dimensional Navier-Stokes equation with a Dirac mass as initial vorticity, .ps
    (with T. Gallay and P.-L. Lions)
    Mathematische Nachrichten, 278(2005), 1665-1672.
  12. On the global wellposedness of the 3-D incompressible Navier-Stokes equations, .pdf
    (with J.-Y. Chemin),
    Annales Scientifiques de l'Ecole Normale Supérieure de Paris,39 (2006), 679-698.
  13. Wellposedness and stability results for the Navier-Stokes equations in R^3, .pdf
    (with J.-Y. Chemin),
    Annales de l'Institut H. Poincaré, Analyse non Linéaire, 26 (2009), no. 2, 599–624.
  14. Remarks on the blow-up of solutions to a toy model for the Navier-Stokes equations, .pdf
    (with M. Paicu),
    Proceedings of the American Mathematical Society, 137 (2009), no. 6, 2075–2083.
  15. Large, global solutions to the Navier-Stokes equations, slowly varying in one direction, .pdf
    (with J.-Y. Chemin),
    Transactions of the American Mathematical Society 362 (2010), no. 6, 2859--2873.
  16. Global regularity for some classes of large solutions to the Navier-Stokes equations, lien sur arxiv
    (with J.-Y. Chemin and M. Paicu),
    Annals of Mathematics 173 (2011), no. 2, 983–1012.
  17. On large perturbations to global solutions of the 3-D incompressible Navier-Stokes equations, lien sur arxiv
    (with J.-Y. Chemin and P. Zhang),
    Journal für die reine und angewandte Mathematik, 681 (2013), 65–82.
  18. A profile decomposition approach to the $L^\infty_t(L^{3}_x)$ Navier-Stokes regularity criterion, pdf
    (with G. Koch and F. Planchon),
    Math. Annalen 355 (2013), no. 4, 1527–1559.
  19. Weak stability of global solutions to the incompressible Navier-Stokes equations, pdf
    (with H. Bahouri),
    Archive for Rational Mechanics and Analysis 209 (2013), no. 2, 569–629.
  20. Blow-up of critical Besov norms at a Navier-Stokes singularity, pdf
    (with G. Koch and F. Planchon),
    Communications in Mathematical Physics, 343 (2016), 39-82.
  21. A non linear estimate on the life span of solutions of the three dimensional Navier-Stokes equations, pdf
    (with J.-Y. Chemin),
    Tunisian Mathematical Journal 1 (2019), 273-293.
  22. On the stability of global solutions to the three dimensional Navier-Stokes equations, pdf
    (with H. Bahouri and J.-Y. Chemin),
    Journal de l'École polytechnique 5 (2018), 843-911.
  23. Some remarks about the possible blow-up for the Navier-Stokes equations, pdf
    (with J.-Y. Chemin and P. Zhang),
    Communications in Partial and Differential Equations, 44 (2019), no. 12, 1387-1405.
  24. Solutions of Navier-Stokes-Maxwell systems in large energy spaces, pdf
    (with D. Arsénio),
    Transactions of the AMS 373 (2020), no. 6, 3853-3884.
  25. On the radius of analyticity of solutions to semi-linear parabolic systems, pdf
    (with J.-Y. Chemin and P. Zhang),
    Math Research Letters, 27 (2020) no. 6, 1631–1643.

Singular perturbation problems

  1. Asymptotics of the solutions of hyperbolic equations with a skew-symmetric perturbation, .ps
    Journal of Differential Equations,150, pages 363-384, 1998.
  2. Applications of Schochet's Methods to Parabolic Equations, .ps
    Journal de Mathématiques Pures et Appliquées, 77, pages 989-1054, 1998.
  3. Ekman boundary layers in rotating fluids, .ps
    (with J.-Y. Chemin, B. Desjardins and E. Grenier)
    ESAIM Controle optimal et calcul des variations, A tribute to J.-L. Lions, 8, pages 441-466, 2002.
  4. On pressureless gases driven by a strong inhomogeneous magnetic field, .ps
    (with L. Saint-Raymond),
    SIAM Journal for Mathematical Analysis, 36 (2005), no. 4, pages 1159-1176.
  5. Weak convergence results for inhomogeneous rotating fluid equations, .pdf
    (with L. Saint Raymond),
    Journal d'Analyse Mathématique, 99(2006), 1-34.
  6. Mathematical Geophysics: An introduction to rotating fluids and to the Navier-Stokes equations,
    (with J.-Y. Chemin, B. Desjardins and Emmanuel Grenier),
    Oxford University Press, 2006.
  7. On the influence of the Earth's rotation on geophysical flows, .pdf
    (with L. Saint-Raymond),
    Handbook of Mathematical Fluid Dynamics, Vol 4, 201-329.
  8. Mathematical study of the betaplane model: equatorial waves and convergence results, .pdf
    (with L. Saint-Raymond),
    Mémoires de la Société Mathématique de France, 107, 2006, vi+116 pages.
  9. Spectral asymptotics for large skew-symmetric perturbations of the harmonic oscillator, lien sur arxiv
    (with Th. Gallay and F. Nier),
    International Mathematics Research Notices 2009 (2009), 2147-2199.
  10. Semiclassical and spectral analysis of oceanic waves, .pdf
    (with C. Cheverry, T. Paul and L. Saint-Raymond),
    Duke Mathematical Journal 161 (2012), no. 5, 845–892.
  11. On the propagation of oceanic waves driven by a strong macroscopic flow, pdf
    (with T. Paul and L. Saint-Raymond),
    Abel Symposia Series.
  12. A singular limit for compressible rotating fluids, pdf
    (with E. Feireisl and A. Novotny),
    SIAM Journal for Mathematical Analysis 44 (2012), 192-205.
  13. Multiscale analysis of compressible viscous and rotating fluids, pdf
    (with E. Feireisl, D. Gérard-Varet and A. Novotny),
    Communication in Mathematical Physics 314 (2012), no. 3, 641–670.
  14. Wellposedness of linearized Taylor equations in magnetohydrodynamics, pdf
    (with D. Gérard-Varet),
    F. Colombini et al (eds.), Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics, Springer INdAM Series 17 (2017), 103-140.
  15. Asymptotics of fast rotating density-dependent incompressible fluids in two space dimensions, pdf
    (with F. Fanelli),
    Revista Matematica Iberoamericana 35 (2019), no. 6, 1763-1807.
  16. On stationary two-dimensional flows around a fast rotating disk, pdf
    (with M. Higaki and Y. Maekawa),
    Math Nachrichten 292 (2019), 273-308.

Dispersive Equations

  1. Profile decomposition for the wave equation outside convex obstacles, .ps
    (with P. Gérard)
    Journal de Mathématiques Pures et Appliquées, 80, pages 1-49, 2001.
  2. On global solutions to a defocusing semilinear wave equation, .ps
    (with F. Planchon)
    Revista Matematica Iberoamericana, 19, pages 161-177, 2003.
  3. On the role of quadratic oscillations in nonlinear Schrodinger equations, .ps
    (with R. Carles and C. Fermanian),
    Journal of Functional Analysis, 203, pages 453--493, 2003.
  4. Analyticity of the scattering operator for semilinear dispersive equations, .pdf
    (with R. Carles),
    Communications in Mathematical Physics, (2009), 286, 3, 1181-1209.
  5. Stability estimates for the near and far field patterns at the high frequency limit, pdf
    (with H. Ammari, H. Bahouri and D. Dos Santos Ferreira),
    Journal of Mathematical Analysis and Applications 400 (2013), no. 2, 525–540.
  6. Universal dynamics for the defocusing logarithmic Schrodinger equation, pdf
    (with R. Carles),
    Duke Mathematical Journal 167 (2018), no. 9, 1761-1801.

Harmonic analysis on Lie groups

  1. Paraproduit sur le groupe de Heisenberg et applications, .ps
    (with H. Bahouri)
    Revista Matematica Iberoamericana, 17, pages 69-105, 2001.
  2. Refined Hardy inequalities, .pdf
    (with H. Bahouri and J.-Y. Chemin),
    Annali della Scuola Normale di Pisa, Vol V (2006), 375-391.
  3. Heat kernel on the Heisenberg group, .pdf
    (with H. Bahouri),
    Progress in nonlinear differential equations and their applications, Birkhauser 78, 2009.
  4. Phase space analysis and pseudodifferential calculus on the Heisenberg group, lien sur arxiv
    (with H. Bahouri and C. Fermanian-Kammerer),
    Astérisque 342 (2012), vi+127pp.
  5. Besov algebras on Lie groups of polynomial growth, pdf
    (with Y. Sire),
    Studia Math. 212 (2012), no. 2, 119–139.
  6. Dispersive estimates for the Schrödinger operator on step 2 Stratified Lie groups, pdf
    (with H. Bahouri and C. Fermanian-Kammerer),
    Analysis of PDE, 9 (2016), 545–574.
  7. Strichartz estimates and Fourier Restriction Theorems on the Heisenberg group, pdf
    (with H. Bahouri and D. Barilari),
    Journal of Fourier Analysis and Applications, 27 (2021), no. 2, 41 pp.
  8. Local dispersive and Strichartz estimates for the Schrödinger operator on the Heisenberg group, pdf
    (with H. Bahouri),
    submitted.
  9. Spectral summability for the quartic oscillator with applications to the Engel group, pdf
    (with H. Bahouri, D. Barilari and M. Léautaud),
    submitted.

Kinetic and hydrodynamic limits

  1. From Newton to Boltzmann : hard spheres and short-range potentials, pdf
    (with L. Saint-Raymond and B. Texier),
    Zurich Advanced Lectures in Mathematics Series, 18 2014 (148 pages).
    A corrected version (a section has been added to Chapter 5) is available here.
  2. The Brownian motion as the limit of a deterministic system of hard-spheres, pdf
    (with T. Bodineau and L. Saint-Raymond),
    Inventiones mathematicae, 203 (2016), 493-553.
  3. From hard spheres dynamics to the Stokes-Fourier equations: an $L^2$ analysis of the Boltzmann-Grad limit, pdf
    (with T. Bodineau and L. Saint-Raymond),
    Annals of PDE 3 (2017), no. 1, Art. 3:2, 118 pp.
  4. One-sided convergence in the Boltzmann-Grad limit, pdf
    (with T. Bodineau, L. Saint-Raymond and S. Simonella),
    Annales de la Faculté des Sciences de Toulouse (6) 27 (2018), no. 5, 985-1022.
  5. Derivation of an Ornstein-Uhlenbeck process for a massive particle in a rarified gas of particles, pdf
    (with T. Bodineau and L. Saint-Raymond),
    Annales Henri Poincaré 19 (2018), no. 6, 1647-1709.
  6. On the convergence of smooth solutions from Boltzmann to Navier-Stokes, pdf
    (with I. Tristani),
    Annales Henri Lebesgue 3 (2020), 561-614.
  7. A microscopic view on the Fourier law, pdf
    (with Th. Bodineau and L. Saint-Raymond),
    Comptes Rendus Physique, Académie des Sciences de Paris, 20 (2019), 402-418.
  8. Fluctuation theory in the Boltzmann-Grad limit, pdf
    (with Th. Bodineau, L. Saint-Raymond and S. Simonella),
    Journal of Statistical Physics 180 (2020), no. 1-6, 873–895.
  9. Statistical dynamics of a hard sphere gas: fluctuating Boltzmann equation and large deviations, pdf
    (with Th. Bodineau, L. Saint-Raymond and S. Simonella),
    submitted.
  10. Long-time correlations for a hard-sphere gas at equilibrium, pdf
    (with Th. Bodineau, L. Saint-Raymond and S. Simonella),
    accepted, Communications on Pure and Applied Mathematics.
  11. Long-time derivation at equilibrium of the fluctuating Boltzmann equation, pdf
    (with Th. Bodineau, L. Saint-Raymond and S. Simonella),
    submitted.
  12. Cluster expansion for a dilute hard sphere gas dynamics, .pdf
    (with T. Bodineau, L. Saint-Raymond and S. Simonella),
    J. Math. Phys. 63 (2022).
  13. Dynamics of dilute gases: a statistical approach, .pdf
    (with T. Bodineau, L. Saint-Raymond et S. Simonella),
    Proceedings of ICM 2022.