Vincent Duchêne

Chargé de recherche au CNRS

Institut de Recherche Mathématique de Rennes — UMR CNRS 6625

Publications Talks    Teaching Miscellaneous Blog    Contact

I am currently Chargé de recherche CNRS, at Institut de Recherche Mathématique, in Rennes, France (IRMAR).

My research is mostly devoted on the mathematical modeling and asymptotic study of various physical problems. An important part of my work deals with the modelization of phenomenons arising in oceanography, with a specific interest in the propagation of internal waves in stratified fluids. I also work on wave propagation in inhomogeneous media, and particularly in highly oscillatory microstructures. See this blog [»] for more details.

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I cannot submit my work to this great new journal, but you should.


[20]  (with T. Iguchi) A Hamiltonian structure of the Isobe-Kakinuma model for water waves, preprint available here.

[19]  (with L. M. Rodrigues) Large-time asymptotic stability of Riemann shocks of scalar balance laws, preprint available here.


The doi link leads to the journal's website, while [xx] gives you the latest preprint.

[18] Rigorous justification of the Favrie-Gavrilyuk approximation to the Serre-Green-Naghdi model, Nonlinearity, 32 (2019) doi

[17]  (with D. Nilsson and E. Wahlén) Solitary wave solutions to a class of modified Green-Naghdi systems, J. Math. Fluid Mech, 20(3) (2018) doi

[16]  (with S. Israwi) Well-posedness of the Green-Naghdi and Boussinesq-Peregrine systems, Ann. Math. Blaise Pascal, 25(1) (2018) doi

[15]  (with N. Raymond) Spectral asymptotics for the Schrödinger operator on the line with spreading and oscillating potentials, Doc. Math., 23 (2018) doi

[14]  The multilayer shallow water system in the limit of small density contrast, Asymptot. Anal., 98(3) (2016) doi

[13]  (with S. Israwi and R. Talhouk) A new class of two-layer Green-Naghdi systems with improved frequency dispersion, Stud. Appl. Math., 137(3) (2016) doi

[12]  (with I. Vukićević and M.I. Weinstein) Oscillatory and localized perturbations of periodic structures and the bifurcation of defect modes, SIAM J. Math. Anal., 47(5) (2015) doi

[11]  (with N. Raymond) Spectral asymptotics of a broken delta-interaction, J. Phys. A: Math. Theor., 47 (2014) doi

[10]  On the rigid-lid approximation for two shallow layers of immiscible fluids with small density contrast, J. Nonlinear Sci., 24(4) (2014) doi

[9]  (with S. Israwi and R. Talhouk) A new fully justified asymptotic model for the propagation of internal waves in the Camassa-Holm regime, SIAM J. Math. Anal., 47(1) (2015) doi

[8]  (with I. Vukićević and M.I. Weinstein) Homogenized description of defect modes in periodic structures with localized defects, Commun. Math. Sci., 13 (3) (2015) doi

[7]  Decoupled and unidirectional asymptotic models for the propagation of internal waves, M3AS:Math. Models Methods Appl. Sci., 24(01) (2014) doi

[6]  (with I. Vukićević and M.I. Weinstein) Scattering and localization properties of highly oscillatory potentials, Comm. Pure Appl. Math., 67(1) (2014) doi

[5]  Asymptotic models for the generation of internal waves by a moving ship, and the dead-water phenomenon, Nonlinearity, 24 (2011) doi

[4] (with M.I. Weinstein) Scattering, homogenization and interface effects for oscillatory potentials with strong singularities, Multiscale Model. Simul., 9 (2011) doi

[3]  Boussinesq/Boussinesq systems for internal waves with a free surface, and the KdV approximation, M2AN Math. Model. Numer. Anal., 46 (2012) doi

[2] (with J. Marzuola and M.I. Weinstein) Wave operator bounds for 1-dimensional Schrödinger operators with singular potentials and applications, J. Math. Phys., 52 (2011) doi

[1]  Asymptotic shallow water models for internal waves in a two-fluid system with a free surface, SIAM J. Math. Anal., 42(5) (2010) doi


[a]  (with S. Israwi and R. Talhouk) Shallow water asymptotic models for the propagation of internal waves, Discrete Contin. Dyn. Syst. Ser. S 7(2) (2014) doi

Some communications

The presentation slides of selected talks are accessible through the '.pdf' link.

June 2018 : Fluid Dynamics and Dispersive Equations Workshop, Lund.
       On the Favrie-Gavrilyuk system as an approximation to the Serre-Green-Naghdi model (.pdf,.mov,.mov,.mov)

June 2017 : Séminaire d'Analyse, Laboratoire de Mathématiques et Physique Théorique, Tours.
       An asymptotic model for the propagation of long waves with improved frequency dispersion (.pdf)

March 2017 : Séminaire "Problèmes Spectraux en Physique Mathématique", Paris.
       Opérateur de Schrödinger avec potentiel oscillant : Potentiel effectif et bifurcation de valeurs propres (.pdf)

Sept. 2016 : Workshop "Recent progress on the qualitative properties of nonlinear dispersive equations and systems", Vienna.
       On the well-posedness of the Green-Naghdi system (.pdf)

Nov. 2015 : Groupe de travail MathOcean, Toulouse.
       Asymptotic limits for the multilayer shallow water system (.pdf)

Oct. 2015 : Colloquium in mathematics (talk for non specialists), Center for Mathematical Sciences, Lund.
       The water waves system and asymptotic models (.pdf)

Nov. 2014 : CAMS seminar, American University of Beirut, Lebanon.
       Kelvin-Helmholtz instabilities in shallow water (.pdf,.mov,.mov)

June 2014 : Nuit des Sciences (talk for general audiences), ENS, Paris.
       Pourquoi ne fait-il par craindre les eaux mortes? (.pdf,.key)

Nov. 2013 : Conference "Modelling, Control and Inverse Problems for the Planet Earth", Paris.
       Asymptotic models for internal waves and the rigid-lid approximation (.pdf)

May 2013 : Groupe de travail Analyse nonlinéaire et EDP, ENS/P6/P7, Paris.
       Complete justification of unidirectional and decoupled models for the propagation of internal waves in oceanography (.pdf)

Jan. 2013 : École thématique GDR CHANT, Transport dans les milieux microstructurés, 7 Laux (Isère, France).
       Trapping waves: Bifurcation of discrete eigenvalues from the edges of the continuous spectrum of the Schrödinger operator (.pdf)

Dec. 2011 : Geometry and Analysis Seminar, Columbia University, New York.
       One-dimensional scattering and localization properties of highly oscillatory potentials (.pdf)

May 2011 : Workshop "Qualitative and numerical aspects of water waves and other interface problems", Vienna.
       The dead-water phenomenon: a nonlinear approach (.pdf)

Feb. 2011 : Applied Mathematics Colloquium, New York.
       Asymptotic models for internal waves in Oceanography (.pdf)


Jan.—March 2019, Lebesgue Master

Master class on shallow-water asymptotic models for water waves

Lecture notes available here (work in progress)

Nov. 2017—Feb. 2018 at ENS Rennes

Reading group on semigroup theory and linear evolution equations

Master's level

Sept.—Nov. 2016 and 2017 at INSA Rennes

Outils mathématiques pour l'ingéenieur

Tutorials, undergraduate level

Sept. 2015—June 2017 at Lycée Chateaubriand, Rennes

Weakly oral examinations, undergraduate level

August 2015 at Institute of Applied Physics and Computational Mathematics, Beijing

Mathematical analysis of models for the propagation of surface and internal waves

Minicourse aimed at PhD students and young researchers

April 2014 at IRMAR, Université de Rennes

Minicourse aimed at PhD students on the Cauchy problem for semilinear dispersive equations

March 2013 at EDST, Université Libanaise, Beirut

Analyse mathématique et modèles asymptotiques en océanographie côtière

2011—2012 at Columbia University

APMAE3101: Linear Algebra

APMAE4001: Principles of Applied Mathematics

2008—2011 at University Paris 6

LM110: Analyse 1 -- Fonctions

LM250: Suites, séries et intégrales

LM260: Séries et intégrales (étude approfondie)


[»]  In this blog, I briefly introduce and motivate my past and present work, and some perspectives.

[ε]  Une vidéo d'introduction aux ondes solitaires hydrodynamiques, dans le cadre des 5 minutes Lebesgue.

[δ]  This is a commented Matlab code, related to article [13]. It numerically computes the bi-layer Green-Naghdi models with improved frequency dispersion derived therein. Please feel free to use and modify it, but let me know in that case!
This is an associated videos illustrating that the classical Green-Naghdi model overestimates Kelvin-Helmholtz instabilities.

[γ]  A note on the well-posedness of the one-dimensional multilayer shallow water model. 8 pages, available only as a preprint, here.

[β]  Le phénomène d'eaux mortes. Introduction au phénomène dans le cadre des Mathématiques de la planète terre 2013.
A rough account on the dead-water phenomenon and my work on the subject, in the context of the Mathematics of Planet Earth 2013 programme.

[α]  Dissertation of my Ph.D. Thesis. Internal waves in oceanography and photonic crystals: a mathematical approach. (Introduction en Français). Les diapositives de la soutenance sont accessibles ici.


IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex (France)

E-mail: vincent.duchene[at]
Phone: (+33) 2 23 23 65 92

— Updated Oct. 03, 2019