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Web page of Aymeric Baradat

Research

Publications

  • Continuous dependence of the pressure field with respect to endpoints for ideal incompressible fluids. pdf, arXiv.
    To appear in Calculus of Variations and Partial Differential Equations.
  • Small noise limit and convexity for generalized incompressible flows, Schrödinger problems, and optimal transport. pdf, arXiv.
    Archive of Rational Mechanics and Analysis.

Preprints

  • Nonlinear instability in Vlasov type equations around rough velocity profiles. pdf, arXiv.
  • On the existence of a scalar pressure field in the Bredinger problem. pdf, arXiv.

PhD

I defended my PhD, entitled Incompressible optimal transport: dependence to the data and entropic regularization and made under the supervision of Yann Brenier and Daniel Han-Kwan in June 2019. Here is the definitive version of the text, and here you can find the slides of the defense (in french).

Talks

  • July 2019: Dependence with respect to the data in incompressible optimal transport.
    MAFRAN Conference, University of Cambridge, UK.
  • June 2019: Dependence with respect to the data in incompressible optimal transport.
    Workshop POTA, Cortona, Italy.
  • November 2018: Entropic regularization of incompressible optimal transport.
    GT CalVa, University Paris 7.
  • October 2018: Entropic regularization of incompressible optimal transport. Slides
    Oberwolfach Seminar: Optimal Transport Theory and Hydrodynamics (from Euler to Monge and vice versa).
  • September 2018: Penrose condition around rough velocity profiles. Slides
    MAFRAN days, University of Cambridge.
  • June 2018: The pressure field in the Brödinger problem.
    GFMUL seminar, University of Lisbon.
  • June 2018: Penrose condition around rough velocity profiles. Slides
    Workshop "Mathematical Advances in Fluid Mechanics", École Polytechnique.
  • June 2018: The Brenier model and the kinetic Euler equation.
    PhD students' seminar of IECL, Université de Lorraine.
  • March 2018: Non-uniqueness in the weak formulation of the Euler equation.
    Working group of the CMLS' analysis team, École Polytechnique.
  • February 2018: Some results about the pressure field in variational models for incompressible fluids. Slides
    MoKaBrainStorm, Université Paris Dauphine.
  • May 2017: Least action principle in an incompressible fluid.
    PhD students' seminar of CMLS and CMAP, École Polytechnique.
  • March 2017: Differential equations and the continuity equation induced by non-Lipschitz vector fields.
    Working group of LJLL and DMA's PhD students in analysis, ENS Paris.

Other productions (in french)

  • Problèmes de minimisation d'entropie avec contraintes.
    (My second master thesis, in probability.) pdf, Slides of the defense.
  • Équation d’Euler et principe de moindre action.
    (An introdution to my field of research.) pdf.
  • Méthodes variationnelles appliquées à la résolution et à l’étude des solutions d’équations de la mécanique des fluides.
    (My first master thesis, in analysis.) pdf.