Research

Publications sorted by thematics (sorted by dates)

Inviscid models:

Stability and existence for the 2D Euler equations:

Dynamics of helical vortex filaments in non viscous incompressible flows, in collaboration with M. Donati and E. Miot,
submitted (preprint).
Inviscid Water-Waves and interface modeling, in collaboration with E. Dormy,
Quart. Appl. Math. 82 (3), 583-637 (2024) (article, preprint).
A homogenized limit for the 2-dimensional Euler equations in a perforated domain, in collaboration with M. Hillairet and D. Wu,
Anal. PDE 15(5), 1131-1167 (2022) (article, preprint).
The vortex method for 2D ideal flows in exterior domains, in collaboration with D. Arsénio and E. Dormy,
SIAM J. Math. Anal. 52(4), 3881-3961 (2020) (article, preprint).
A note on the regularity of the holes for permeability property through a perforated domain for the 2D Euler equations, in collaboration with C. Wang,
Sci. China Math. 62(6), 1121-1142 (2019) (article, preprint).
Dynamics of rigid bodies in a two dimensional incompressible perfect fluid, in collaboration with O. Glass, A. Munnier and F. Sueur,
J. Differential Equations 267(6), 3561-3577 (2019) (article, preprint).
Asymptotic behavior of 2D incompressible ideal flow around small disks, in collaboration with M. C. Lopes Filho and H. J. Nussenzveig Lopes,
Asymptot. Anal. 108(1-2), 45-83 (2018) (article, preprint).
On the motion of a small light body immersed in a two dimensional incompressible perfect fluid with vorticity, in collaboration with O. Glass and F. Sueur,
Comm. Math. Phys. 341(3), 1015-1065 (2016) (article, preprint).
Impermeability Through a Perforated Domain for the Incompressible two dimensional Euler Equations, in collaboration with N. Masmoudi,
Arch. Ration. Mech. Anal. 221(3), 1117-1160 (2016) (article, preprint).
The Two Dimensional Euler Equations on Singular Exterior Domains, in collaboration with D. Gérard-Varet,
Arch. Ration. Mech. Anal. 218(3), 1609-1631 (2015) (article, preprint).
Permeability through a perforated domain for the incompressible 2D Euler equations, in collaboration with V. Bonnaillie-Noel and N. Masmoudi,
Ann. Inst. H. Poincaré Anal. Non Linéaire 32(1), 159-182 (2015) (article, preprint).
The vortex method for 2D ideal flows in the exterior of a disk, in collaboration with D. Arsenio and E. Dormy,
Journée équations aux dérivées partielles, (Roscoff 2014), Exp. No. 5, 22 p. (article, preprint).
On the motion of a small body immersed in a two dimensional incompressible perfect fluid, in collaboration with O. Glass and F. Sueur,
Bull. Soc. Math. France 142(3), 489-536 (2014) (article, preprint).
The Two Dimensional Euler Equations on Singular Domains, in collaboration with D. Gérard-Varet,
Arch. Ration. Mech. Anal. 209(1), 131-170 (2013) (article, preprint).
Two Dimensional Incompressible Ideal Flow Around a Small Curve,
Comm. Partial Differential Equations 37(4) , 690-731 (2012)(article, preprint).
Fluide idéal incompressible en dimension deux autour d'un obstacle fin,
Séminaire Équations aux dérivées partielles (Polytechnique) (XEDP, 2008-2009), Exp. No. 24, 13 p. (article).
Two Dimensional Incompressible Ideal Flow Around a Thin Obstacle Tending to a Curve,
Ann. Inst. H. Poincaré Anal. Non Linéaire 26(4), 1121-1148 (2009) (article, preprint).

Uniqueness for the 2D Euler equations:

The vortex-wave system with gyroscopic effects, in collaboration with E. Miot,
Ann. Scuola Norm. Sup. Pisa Cl. Sci. 22(5), 1-30 (2021) (article, preprint).
The Euler Equations in Planar Domains with Corners, in collaboration with A. Zlatos,
Arch. Ration. Mech. Anal. 234(1), 57–79 (2019) (article, preprint).
Uniqueness for Two Dimensional Incompressible Ideal Flow on Singular Domains,
SIAM J. Math. Anal. 47(2), 1615-1664 (2015) (article, preprint).
Uniqueness for the two-dimensional Euler equations on domains with corners, in collaboration with E. Miot and C. Wang,
Indiana Univ. Math. J. 63(6), 1725-1756 (2014) (article, preprint).
Incompressible flow around thin obstacle/Uniqueness for the vortex-wave system,
Journée équations aux dérivées partielles, (Evian 2009), Exp. No. 4, 17 p. (article).
Uniqueness for the vortex-wave system when the vorticity is constant near the point vortex, in collaboration with E. Miot,
SIAM J. Math. Anal. 41(3), 1138-1163 (2009) (article, preprint).

Other models related to perfect fluid:

Bloch-Floquet band gaps for water waves over a periodic bottom, in collaboration with M. Ménard and C. Sulem,
submitted (preprint).
Dynamics of several point vortices for the lake equations, in collaboration with L.E. Hientzsch and E. Miot,
Trans. Amer. Math. Soc. 377(1), 203-248 (2024) (article, preprint).
Degenerate lake equations: classical solutions and vanishing viscosity limit, in collaboration with B. Al Taki,
Nonlinearity 36(1), 653-678 (2023) (article, preprint).
Lake equations with an evanescent or emergent island, in collaboration with L.E. Hientzsch and E. Miot,
Commun. Math. Sci. 20(1), 85-122 (2022) (article, preprint).
Bloch theory and spectral gaps for linearized water waves, in collaboration with W. Craig, M. Gazeau and C. Sulem,
SIAM J. Math. Anal. 50(5), 5477–5501 (2018) (article, preprint).
Interactions between moderately close inclusions for the 2D Dirichlet-Laplacian, in collaboration with V. Bonnaillie-Noel and M. Dambrine,
Appl. Math. Res. Express. AMRX 2016(1), 1-23 (2016) (article, preprint).
Topography influence on the Lake equations in bounded domains, in collaboration with T. Nguyen and B. Pausader,
J. Math. Fluid Mech. 16(2), 375-406 (2014) (article, preprint).

Viscous fluid:

Stability for the Navier-Stokes equations:

The vanishing viscosity limit for 2D Navier-Stokes in a rough domain, in collaboration with D. Gérard-Varet, T. Nguyen and F. Rousset,
J. Math. Pures Appl. 119, 45-84 (2018) (article, preprint).
Small moving rigid body into a viscous incompressible fluid, in collaboration with T. Takahashi,
Arch. Ration. Mech. Anal. 223(3), 1307-1335 (2017) (article, preprint).
The vanishing viscosity limit in the presence of a porous medium, in collaboration with A. Mazzucato,
Math. Ann. 365(3-4), 1527-1557 (2016) (article, preprint).
3D Viscous Incompressible Fluid around One Thin Obstacle,
Proc. Amer. Math. Soc. 143(5), 2175-2191 (2015) (article, preprint).
Two Dimensional Incompressible Viscous Flow Around a Thin Obstacle Tending to a Curve,
Proc. Roy. Soc. Edinburgh Sect. A 139(6), 1237-1254 (2009) (article, preprint).

Long time behavior for the solutions to the Navier-Stokes equations:

Large time behavior for the 3D Navier-Stokes with Navier boundary conditions, in collaboration with J. Kelliher, M. Lopes Filho H. Nussenzveig Lopes and E. Titi,
submitted (preprint).
Asymptotics of solutions to the Navier-Stokes system in exterior domains, in collaboration with D. Iftimie and G. Karch,
J. London Math. Soc. 90(3), 785-806 (2014) (article, preprint).
Long-time behavior for the two-dimensional motion of a disk in a viscous fluid, in collaboration with S. Ervedoza and M. Hillairet,
Comm. Math. Phys. 329(1), 325-382 (2014) (article, preprint).
Self-similar asymptotics of solutions to the Navier-Stokes system in two dimensional exterior domain, in collaboration with D. Iftimie and G. Karch,
sur Arxiv (preprint).

Phd topic

During my Phd, I have studied the influence of a thin obstacle on the behavior of incompressible flow, when the obstacle tends to a curve or a surface. The small obstacle limit is an instance of the general problem of PDE on singularly perturbed domains. There is a large literature on such problems, specially in the elliptic case. Asymptotic behavior of fluid flow on singularly perturbed domains is a natural subject for analytical investigation which is virtually unexplored.
The first works were made in 2003 and 2006 by Iftimie, Lopes Filho and Nussenzveig Lopes concerning two dimensional incompressible ideal flow (governed by the Euler equations) and viscous flow (governed by the Navier-Stokes equations) when the obstacle shrink homothetically to a point. Iftimie and Kelliher worked in 2008 on the three dimensional incompressible viscous flow around an obstacle which shrink to a point.
My thesis brings together all my works concerning incompressible ideal and viscous flow around a curve (in 2D) and around a surface (in 3D). We finish by giving uniqueness of the vortex-wave system with a single point vortex introduced by Marchioro and Pulvirenti, in the case where the initial vorticity is constant near the point vortex (Phd thesis).

HDR topic

We bring together in this thesis the results obtained by the author and his collaborators. We give here the main ideas of the analysis developed for their proofs.
Our concern in the first part is the convergence of solutions to the two-dimensional Euler equations when we perturb the domain geometry. Depending on the perturbation, we will get the stability or a limit verifying a modified system. We will discuss in the second part about the uniqueness issue for these perturbed systems.
We will also study the stability of solutions to the Navier-Stokes equations. First, we will mention the case of small obstacles. Next, we will focus on the long time behavior for the solutions. These two questions are in fact related through the scaling property of the equations governing viscous fluids. (HDR thesis).

Collaborations and invitations

D. Arsénio (Paris 7) and E. Dormy (ENS Paris) : several visits at Paris since 2016, visit at Abu Dhabi (1 week in November 2014 and 1 week in October 2022) and visits at Cambridge (1 week in February 2020, 1 week in March 2022 and 1 week in May 2022)).
V. Bonnaillie-Noel (Rennes): visits at Rennes (1 week in February 2011, 2 weeks in March 2012, 1 week in April 2013 and 1 week in April 2014).
W. Craig (McMaster, Canada), M. Gazeau and C. Sulem (Toronto, Canada): visits in Ontario (3 weeks in July 2011, 7 weeks in summer 2012, 3 weeks in May 2013, 2 months in summer 2014, 2 weeks in August 2017 and 2 weeks in November 2022).
M. Dambrine (Pau) : visit at Pau (1 week in May 2014).
V. Duchène and M. Rodrigues (Rennes, France) : visit at Rennes (1 week in March 2016).
S. Ervedoza (Toulouse, France) and M. Hillairet (Montpellier): visits at Toulouse (1 week in October 2009 and 1 week in May 2010), at Montpellier (1 week in February 2015, 1 week in February 2016, 1 week in November 2017, 1 week in April 2018, 1 week in October 2019 and 1 week in January 2024).
D. Gérard-Varet (Paris 7): 2010-...
O. Glass (Paris Dauphine), A. Munnier (Nancy) and F. Sueur (Bordeaux) : visit at Bordeaux (1 week in Decembre 2014 and 1 week in April 2018), at Nancy (1 week in May 2016).
D. Iftimie (Lyon) and G. Karch (Wroclaw, Pologne) : several visits at Lyon (2013).
M.C. Lopes Filho and H.J. Nussenzveig Lopes (Campinas and Rio, Brazil): visits at Campinas (1 month in Frebruary 2009 and 2 weeks in November 2010), at Lyon (1 week in July 2009 and 1 week in December 2009) and at Rio de Janeiro (2 weeks in December 2012, 3 weeks in November 2018 and 2 weeks in November 2019).
N. Masmoudi (New-York University-Courant Institut): visits at New-York (2 weeks in October 2012 and 1 week in October 2013).
A. Mazzucato (Penn State University, USA): visit at Penn State College (1 week in November 2011).
E. Miot (Polytechnique, Paris): 2008-...
B. Pausader and T. Nguyen (Brown and PennState, USA): visit at Brown (2 weeks in November 2010, 1 week in December 2018 and 2 weeks in November 2021), at New-York University-Courant Institut (2 weeks in November 2011) and at PennState University (2 weeks in October 2013, 1 week in November 2017).
T. Takahashi (Nancy): visit at Nancy (1 week in April 2015).
A. Vasseur (Austin, USA) : visit at Austin (2 weeks in April 2024).
C. Wang (Peking University, China): visit at Beijing (1 month in December 2016, 2 weeks in December 2017 and 2 weeks in December 2018).
A. Zlatos (San Diego, USA): visit at Wisconsin-Madison (1 week in December 2015) and at San Diego (1 week in December 2019).

Seminars and conferences

My last talks given in conferences:

Journées Maths et géosciences (Chambéry, France, November 2024) : Modélisation de l'équation des vagues.
Journées EDP Auvergne-Rhône-Alpes (Grenoble, France, November 2024) : Modélisation de l'équation des vagues.
Conference "Fluid Equations, A Paradigm for Complexity: Regularity vs Blow-up, Deterministic vs Stochastic" (Banff, Canada, October 2023) : Point vortex for the lake equations.

Recent seminars:

Séminaire de l'équipe d'Analyse Appliquée de l'I2M (Marseilles, France, January 2025) : Modélisation de l'équation des vagues.
Groupe de travail MathsInFluids (ENS Lyon, France, September 2024) : Modélisation de l'équation des vagues.
Séminaire EDP (Rennes, France, June 2024): Modélisation de l'équation des vagues.
Analysis Seminar (University of Texas at Austin, USA, March 2024): On the vortex filament conjecture.
Séminaire MACS (modélisation, analyse et calcul scientifique) (Lyon, France, March 2024): Sur la conjecture des filaments de tourbillons.
Séminaire à ISTerre (Chambery, France, February 2024): Utilisation d'outils mathématiques en géosciences.
Séminaire de l'équipe ACSIOM (Montpellier, France, January 2024): Points vortex pour les équations des lacs..
Séminaire de l'équipe EDPs2 (Chambery, France, December 2023): Points vortex pour les équations des lacs.
Seminar in the program "Order and Randomness in Partial Differential Equations" (Institut Mittag-Leffler, Sweden, November 2023): Modeling inviscid water waves.

(Update: 4th October 2024)