David Gérard-Varet

Professor of Mathematics, Université Paris Diderot
Member of Institut de Mathématiques de Jussieu - Paris Rive Gauche
Address:
Université Paris Diderot, UFR de Mathématiques
Bâtiment Sophie Germain, Bureau 724
75205 Paris Cedex 13
Phone : +33 1 57 27 92 84
Mail : david(dot)gerard-varet(at)imj-prg(dot)fr


Research Interests

Partial differential Equations,
Fluid mechanics, boundary layers, instabilities in hydro- and magnetohydrodynamics, singular perturbation problems, homogenization.



Papers

Nonlinear boundary layers for rotating fluids (with A-L. Dalibard)
Submitted.

Boundary layer for a non-newtonian flow over a rough surface (with A. Wroblewska-Kaminska)
Submitted.

Landau damping for the Kuramoto model (with B. Fernandez, G. Giacomin)
To appear, Ann. Henri Poincaré.

Phénomène d'amortissement dans les équations d'Euler (d'après Bedrossian-Masmoudi) (in french)
Séminaire Bourbaki, 67ème anné, 2014-205, nº 1091.

Well-posedness for the Prandtl system without analyticity or monotonicity (with N. Masmoudi)
To appear, Ann. Sci. Ecole Norm. Sup.

The two-dimensional Euler equations on singular exterior domains (with C. Lacave)
Arch. Rat. Mech. Anal. 218,1609--1631 (2015).

Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries II (with D. Han-Kwan, F. Rousset)
J. Ecole Polytechnique 1, 343--386 (2014).

Rough wall effect on micro-swimmers (with L. Giraldi)
ESAIM: Control, Optimisation and Calculus of Variations. 21, 757--788 (2015).

The influence of boundary conditions on the contact problem in a 3d Navier-Stokes flow (with M. Hillairet, C. Wang)
103, 1--38 (2015). Journal Math. Pures Appl.

Computation of the effective slip of rough hydrophobic surfaces via homogenization (with M. Bonnivard, A-L. Dalibard)
M3AS. M3AS 24, 2259--2285 (2014).

Existence of weak solutions up to collision for viscous fluid-solid systems with slip (with M. Hillairet)
Comm. Pure Appl. Math. 67, 2022--2075 (2014).

On shape optimization problems involving the fractional laplacian (with A-L. Dalibard)
ESAIM: Control, Optimisation and Calculus of Variations. 19, 976--1013 (2013).

Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries (with D. Han-Kwan, F. Rousset)
Indiana Univ. Math. Journal. 62, 359--402 (2013).

The 2D Euler equation on singular domains (with C. Lacave)
Arch. Rat. Mech. Anal. 209,131--170 (2013).

Multi-scale analysis of compressible viscous and rotating fluids (with E. Feireisl, I. Gallagher, A. Novotny)
Comm. Math. Phys. 314, 641--670 (2012).

Computation of the drag force on a rough sphere close to a wall (with M. Hillairet)
M2AN 46, 1201--1224 (2012).

Remarks on the ill-posedness of the Prandtl Equation (with T. NGuyen)
Asymptotic Analysis 77, 71--88 (2012).

Homogenization and boundary layers (with N. Masmoudi)
Acta Math. 209, 133-178 (2012).

Effective boundary condition at a rough surface starting from a slip condition (with A-L. Dalibard)
Journal of Differential Equations 251, 3297-3658 (2011).

Homogenization in polygonal domains (with N. Masmoudi)
J. Eur. Math. Soc.. 13, 1477-1503 (2011).

On the ill-posedness of the Prandtl equation (with E. Dormy)
J. Amer. Math. Soc. 23, 591-609 (2010).

Relevance of the slip condition for fluid flows near an irregular boundary (with N. Masmoudi)
Comm. Math. Phys. 295, 99-137 (2010).

Regularity issues in the problem of fluid structure interaction (with M. Hillairet)
Arch. Rat. Mech. Anal. 19, 375-407 (2010).

The Navier wall law at a boundary with random roughness
Comm. Math. Phys. 286, 81-110 (2009)

Time scales separation for dynamo action (with E. Dormy)
EuroPhysics Letter 81 64002 (2008).

Wall laws for fluid flows at a boundary with random roughness (with A. Basson)
Comm. Pure Applied Math. 61 No.7, 941-987 (2008)

Three-dimensional instability of planar flows (with F. Gallaire, F. Rousset)
Arch. Rat. Mech. Anal. 186, No.3, 423-475 (2007)

Remarks on boundary layer expansions (with T. Paul)
Comm. Partial Diff. Eq. 33, No.1-3, 97-130 (2008)

Weakly nonlinear analysis of the alpha effect
Geophysical and Astrophysical Fluid Dynamics 101, 171-184 (2007)

On compressible Navier-Stokes equations with density dependent viscosities in bounded domains (with D. Bresch, B. Desjardins)
J. Math. Pures Appl. 87 (9), 227-235 (2007)

Shear layer solutions of incompressible MHD and dynamo effect (with F. Rousset)
Ann. I.  H. Poincaré / Anal. non lin. 24 (5), 677-710 (2007)

Homogenization problems from shallow water theory   (with D. Bresch)
Appl. Math. Lett. 20  no. 5, 505510 (2007)

Ekman layers near wavy boundaries (with E. Dormy)
J. Fluid Mech. 565, 115-134 (2006)

Derivation of the planetary geostrophic equations (with D. Bresch, E. Grenier)
Arch. Rat. Mech. Anal. 182, No.3, 387413 (2006)

Oscillating solutions of incompressible MHD and dynamo effect
SIAM Journal Math. Anal. 37, No.3, 815840 (2005).

Mathématiques Marines (with D. Bresch, B. Desjardins).  La Recherche, Mars 2005.

About roughness-induced effects on the quasi-geostrophic model (with D. Bresch)
Comm. Math. Phys. 253, 179200. No.1, 81119 (2005).
Un résumé de cet article fait l'objet de l'acte de conférence : Roughness Induced Effects in Geophysics (with D. Bresch),
School and Workshop on Oceanography, Lakes and Rivers, Centro international de Matematica 25 (2004).

Formal derivation of boundary layers in fluid mechanics.
J. Math. Fluid Mech. no. 2, 179200 (2005)
Prolongement de l'acte de conférence :  A zoology of boundary layers (with E. Grenier), Mathematics and environment, RACSAM 96 (2002).

Rotating fluids in a cylinder (with D. Bresch, B. Desjardins)
Disc.Cont.Dyn.Sys.- Series A  1, 4782, (2004).

Highly rotating fluids in rough domains.
J. Math. Pures Appl. 
82, 14531498 (2003).
Un résumé de cet article fait l'objet de l'acte de conférence :  Convergence of the rotating fluids system in a domain with rough boundaries 
Journées "Equations aux Dérivées Partielles"
, Exp. No VIII, 15, Univ. Nantes, Nantes (2003).

A geometric optics type approach to fluid boundary layers.
Comm. Partial Diff. Eq
  28,  16051626 (2003).

Amplification of small perturbations in a Hartmann layer.
Physics of Fluids 14,  No. 4,  14581467 (2002).