Research

One of my main topic of research is the issue of well-posedness for systems of first-order, quasilinear PDEs. The focus is on properties of the spectrum of the principal symbol of the system – reality of the spectrum, crossing of eigenvalues. In the cases of non-reality of the spectrum, I prove an Hadamard instability in Gevrey spaces, hence pointing out the strong, local ill-posedness of such systems. In some cases of crossing of real eigenvalues, I prove an energy estimate in Gevrey spaces.

In collaboration with Jonathan Ben-Artzi in the QUEST project, I work in kinetic theory. We are interested in many features of Vlasov-Poisson and Vlasov-Maxwell equations: Landau damping, time-decay of plasmas, micro- to mesoscopic limit…

I started recently a collaboration with Francesco Fanelli from Institut Camille Jordan (Lyon) on the wide and interesting topic of Gevrey well-posedness and inviscid limits in Gevrey regularity for different types of hydrodynamic systems, such as active scalar equations or inhomogeneous Euler equations.

You can find my (french) curriculum here.

Publications

  1. Averaging along degenerate flows on the annulus, with Jonathan Ben-Artzi (arxiv), 2019.
  2. Uniform convergence in von Neumann’s ergodic theorem in absence of a spectral gap, with Jonathan Ben-Arzti (arxiv), 2019.
  3. On hyperbolicity and Gevrey well-posedness. Part three: a class of weakly hyperbolic systems (arxiv – to appear in Indiana University Mathematics Journal ), 2018.
  4. On the action of pseudo-differential operators on Gevrey spaces, 2017 (pdf , arxiv).
  5. On hyperbolicity and Gevrey well-posedness. Part two: scalar or degenerate transitions, 2017 (pdf , arxiv – accepted in Journal of Differential Equations).
  6. On hyperbolicity and Gevrey well-posedness. Part one: the elliptic case, 2016 (pdf , arxiv).

Recent Talks

  1. 2018 December 14th: SWAP at Bath.
  2. 2018 November 22nd: Séminaires Equations aux Dérivées Partielles at the Laboratoire de Mathématiques de Besançon
  3. 2018 April 24: Geometry and Analysis Seminar at QMUL, London.
  4. 2018 February 21st: Network on Hyperbolic Equations in Loughbourough.
  5. 2018 February 12th: GAPDE Seminar at Cambridge.
  6. 2017 November 28th: Seminaire Analyse-EDP de l’Institut Camille Jordan (Lyon, France).
  7. 2017 November 16th: Pure Analysis and PDEs Seminar at Imperial College (London, UK).
  8. 2017 October 2nd: Cardiff University Analysis Seminar.

Grants

  1. 2018 November: LMS Scheme 4 Grant “Research in Pairs” for a two weeks visit in Lyon for a collaboration with Francsco Fanelli.
    Total amount: £1200.
  2. 2018 June: LMS Scheme 1 Grant to organize the Conference An Analyst, a Geometer and a Probabilist walk into a bar with Jonathan Ben-Artzi in Cardiff in June 2018.
    Total amount: £6000.

Thesis

  1. Le problème de Cauchy pour les systèmes quasi-linéaires faiblement hyperboliques ou non-hyperboliques en régularité Gevrey, 2017 (pdf).
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