Y. Brenier

Directeur de recherches au CNRS


DMA (UMR 8853), ECOLE NORMALE SUPERIEURE, 45 rue d'Ulm, 75005 Paris, France
E-mail: yann.brenier at ens.fr
TELEPHONE: +33 1 44 32 20 90

  • Die Mathematiker sind eine Art Franzosen: Redet man zu ihnen, so uebersetzen sie es in ihre Sprache, und dann ist es alsobald ganz etwas anders ( Goethe, Maximen und Reflektionen XVI, 1005). Les mathematiciens sont comme les francais : quoique vous leur dites, ils le traduisent dans leur propre langue et le transforment en quelque chose de totalement different. Mathematicians are like Frenchmen: whatever you say to them they translate into their own language, and forthwith it is something entirely different.

  • EULER 1755 (The Euler Archives http://www.math.dartmouth.edu/~euler/ LOOK AT INDEX NUMBER 226: Principes generaux du mouvement des fluides
  • FEYNMAN'S NOBEL LECTURE 1965
    COURS FIMFA EDP 2018/2019
  • Chapitre introductif
  • Chapitre sur les equations de transport lineaires.
  • (Reference recente sur les champs peu reguliers : niveau M2+)
  • Chapitre sur les methodes de minimisation pour les equations elliptiques (version corrigee, dernieres corrections 15/01/19)
  • Chapitre "du parabolique a l'hyperbolique" (version completee, 13/12/18)
  • Chapitre "systemes entropiques de lois de conservation" (version corrigee, dernieres corrections 15/01/19)
  • Enonce et corrige examen

    Oberwolfach Seminar October 2018
  • Chapter 1
  • Chapter 2
  • Chapter 3
  • Chapter 4

    TALKS
  • Convex optizimation method for the IVP, Colloque franco-roumain, Bordeaux 2018 (pdf)
  • The Arctangential heat equation, ICMS Edinburgh 2018 (pdf)
  • Transparents: Monge-Ampere Gravitation, Warwick 2016 (pdf)
  • Transparents: Topology-preserving diffusion of divergence-free vector fields 2012 (pdf)
  • Transparents: A modified action for the EUR problem 2010 (pdf)
  • Transparents: Rearrangement Convection Competition 2009 (pdf)
  • Slides: Hidden Convexity in Geometric PDEs (pdf)
  • Slides: On the field-matter interaction in Electrodynamics: A weak convergence approach ("Des EDP au calcul scientifique", en l'honneur de Luc Tartar, Paris 2-6/07/2007) (pdf)
  • Slides: L2 formulation of multid scalar conservation laws 2007 (pdf)
  • Slides: String integration of some MHD equations (Aziz lectures 2006) (pdf)
  • The melting rubik cube : IPAM-UCLA 2018 (video)
    PAPERS pdf files, generally not in final form. Look at
  • HAL and
  • ARXIV websites for more recent papers.
  • A modified least action principle for the early universe reconstruction problem 2010 (pdf)
  • (YB and Mike Cullen) Rigorous derivation of the x-z semigeostrophic equations 2009 (pdf) -final version in CMS 2009
  • Optimal Transport, Convection, Magnetic Relaxation and Generalized Boussinesq Equations 2007 (pdf) -final version in JNLS 2009
  • Generalized solutions and hydrostatic approximation of the Euler equations (pdf) -final version in Physica D 2008
  • L2 formulation of multidimensional scalar conservation laws 2006 (pdf) -final version in Archive Rat. Mech. Analysis 2009-BUT NOTICE THAT
  • THIS FORMULATION HAD ALREADY BEEN FOUND BEFORE BY I. PANOV !!!
  • as explained in Perepelitsa's 2014 paper.
  • semi-relativistic strings (pdf) -See final version in. Methods Appl. Anal. 2005
  • Seminaire X-EDP 2005 (pdf)
  • (Francois Bolley, YB and Gregoire Loeper) Contractive metrics for scalar conservation laws (pdf) -final version in J. Hyp.Diff. Equ.2005
  • (YB and Wen-An Yong) derivation of particle, string and membrane motions from the Born-Infeld electromagnetism (pdf)-See final version in J. Math. Physics 2005
  • (YB and Gregoire Loeper) A geometric approximation to the Euler equations: the Vlasov-Monge-Ampere system (pdf) -final version in GAFA 2004
  • Order preserving vibrating strings and applications to Electrodynamics and Magnetohydrodynamics (pdf) -See final version in. Methods Appl. Anal. 2004
  • Deformations of 2D fluid motions using 3D Born-Infeld equations (pdf) - See final version in Monatsh. Math 2004: http://link.springer.de
  • Hydrodynamic structure of the augmented Born-Infeld equations (pdf) - See final version in Archive Rat. Mech. Analysis 2004: http://link.springer.de
  • (Y.B., R. Natalini, M. Puel) Relaxation of the incompressible Navier-Stokes equations (pdf) -See final version in Proc. Amer. Math. Soc. 2004
  • (YB, Frisch, Henon, Loeper, Matarrese, Mohayaee, Sobolevskii) Reconstruction of the early universe -See final version in Mon. Not. R. Astron. Soc. 2003 (pdf)
  • Hydrostatic limit of the Euler equations -see final version in Bull. Sci. Math. 2003 (pdf)
  • (Y.B., N. Mauser, M. Puel) Derivation of e-MHD from the Vlasov-Maxwell system - (pdf) -See final version in Commun. Math. Sci. 2003
  • CIME 2001 lecture : Extended Monge-Kantorovich theory (pdf)
  • Harmonic functions up to rearrangement and isothermal gas dynamics (pdf file-See final version in Comm. Math. Sc. 2003)
  • Topics on Hydrodynamics and volume preserving maps (pdf)-See final version in Handbook of mathematical fluid dynamics, Vol. II, North-Holland 2003)
  • Osherfest 2002 : Permutations and PDEs (pdf)
  • conference ICM 2002 (pdf)
  • A caricature of Coulomb interaction (pdf file-See final version in Comm. Math. Physics 2000)
  • From Vlasov-Poisson to Euler (pdf file-See final version in Comm. PDEs 2000)
  • expose SMF 1999 (pdf file-en francais)
  • (Y.B. and J.-D.Benamou) Computational solution to the Monge-Kantorovich problem (pdf file-See final version in Numerische Math.2000)
  • Hydrostatic flows with convex velocity profiles (pdf file-See final version in Nonlinearity 1999)
  • Geodesics on groups of volume preserving maps (pdf file-See final version in CPAM 1999)
  • (Y.B. and E.Grenier) Sticky particles (pdf file-See final version in SINUM 1998)
    NUMERICAL SIMULATIONS AND ANIMATIONS
    Illustration for paper 'Computational solution to the Monge-Kantorovich problem' Monge-Kantorovich mass transfer on the 2-torus
    Illustration for a paper to be written!
    Illustration for paper 'L2 formulation of multidimensional scalar conservation laws'
    Illustration for paper 'Order preserving vibrating strings and applications to Electrodynamics and Magnetohydrodynamics'
    Illustration for paper 'Order preserving vibrating strings and applications to Electrodynamics and Magnetohydrodynamics'
    Illustration for paper 'Geodesics on groups of volume preserving maps' : 3 examples of shortest paths between permutations (approximating measure preserving maps on the unit interval)
    NB : the second one can be computed analytically.
    NB : the first one vaguely looks like a rotating Matterhorn viewed from different angles (Gornergrat>Zermatt>Schoenbielhuette)
    Illustration for a paper to be written!
    Illustration for a paper to be written!
    Example of a harmonic map on the unique square valued in the set of measure preserving maps on the unit interval (approximated by permutations)
    A dissipative solution of the pressureless Euler-Poisson system on the real line. A neutralizing background is fixed on the unit interval. The initial density is uniform on the unit interval. The initial velocity at time t=0 and point x is v=4*sin(2*r*pi*(x-a))


    MISCELLANEOUS DOCUMENTS