Research
On this page, you will find my publication list follows, with online links towards all my published works. For further details, please consult my CV and my list of publications.
Publications
This section contains links to my papers. When an article is only available on the journal's website through a paying subscription, the link points to the final preprint instead.
Articles published in international reviewed journals
F. Vigneron. Spatial Decay of the Velocity Field of an Incompressible Viscous Fluid in Rd. Nonlinear Analysis T.M.A., Vol. 63/4 (2005), 525-549.
L. Brandolese, F. Vigneron. On the Localization of the Magnetic and the Velocity Fields in the MHD Equations. Proceedings of the Edinburgh Math. Soc., Vol. 137/3 (2007), 475- 495.
L. Brandolese, F. Vigneron. New Asymptotic Profiles of Nonstationary Solutions of the Navier-Stokes System. J. de Mathématiques Pures et Appliquées, Vol. 88/1 (2007), 64-86.
S. Mustapha, F. Vigneron. Construction of Sobolev Spaces of Fractional Order with Sub-Riemannian Vector Fields. Annales de l’Institut Fourier, Vol. 57/4 (2007).
F. Vigneron. The Trace Problem for Weighted Sobolev Spaces over the Heisenberg Group. J. d’Analyse Mathématique, Vol. 103/1 (2007), 279-306.
F. Vigneron. Free Turbulence on R3 and T3. Dynamics of PDE, Vol. 7/2 (2010), 107-160.
R. Hadiji, F. Vigneron, S. Bae, H. Yazidi. A non-linear problem involving a critical Sobolev exponent. J. of Mathematical Analysis and Applications, Vol. 396/1 (2012), 98-107.
C. Imbert, R. Shvydkoy, F. Vigneron. Global Well-Posedness of a Non-Local Burgers Equation: The Periodic Case. Annales Mathématiques de Toulouse, Sér. 6, Vol. 25/4 (2016), 723-758.
S. Seuret, F. Vigneron. Multifractal Analysis of Functions on Heisenberg and Carnot Groups. J. of the Institute of Mathematics of Jussieu, Vol. 16/1 (2017), 1-38.
H. Bahouri, F. Vigneron. Analyse fréquentielle du signal. Images des Mathématiques. Échos de la recherche (Jan. 5, 2019). The linked version of this article is interactive; here is a printable static version (48 pages).
R. Hadiji, F. Vigneron. Existence of Solutions of a Non-Linear Eigenvalue Problem with a Variable Weight. J. of Differential Equations, 266/2-3 (2019), 1488-1513.
F. Vigneron. Apprendre Autrement : le point de vue d’un mathématicien sur la création d’un parcours de licence. Gazette des Mathématiciens, 160 (April 2019), 41-52 [in french].
F. Vigneron. A simple proof of the Hardy inequality on Carnot groups and for some hypoelliptic families of vector fields. To appear in the Tunisian Journal of Mathematics (2019).
C. Imbert, R. Tahrini, F. Vigneron. Regularity of solutions of a fractional porous medium equation. Interfaces and Free Boundaries, 22/4 (2020), 401-442.
I. Vasilyev, F. Vigneron. Variation on a theme by Kiselev and Nazarov : Hölder estimates for non-local transport-diffusion, along a non divergence-free BMO field. J. of the Institute of Mathematics of Jussieu, (2021) 1-25.
H. Bahouri, Z. Lyu, F. Vigneron. Bubble and Profile Decompositions Methods : a Common Thread Through Many Works in Geometry, Physics and Fluid Mechanics. To appear in Morningside Lectures in Mathematics, Vol. 6 (2022).
N. Lerner, F. Vigneron. On some properties of the curl operator that are of consequence for the Navier-Stokes system. Comm. in Math. Research, Vol. 38 (2022), 449-497.
R. Anton, N. Mihalache and F. Vigneron. A short ODE proof of the Fundamental Theorem of Algebra. The Mathematical Intelligencer (24 nov. 2023).
Articles submitted in international reviewed journals
19. F. Vigneron. On the Wiener-Khinchin transform of functions that behave as approximate power-laws. Applications to fluid turbulence. Preprint hal-02284557 / arXiv:1909.06078.
20. J. Tan, F. Vigneron. Global well-posedness and long-time asymptotics of a general nonlinear non-local Burgers Equation. Preprint hal-03468023 (2021).
21. R. Anton, N. Mihalache and F. Vigneron. Fast evaluation of complex polynomials. Preprint hal-03820369 / arXiv:2211.06320 (2022). See also the documentation of the associated GitHub project (item [23]).
Proceedings
22. F. Vigneron. Espaces de Sobolev d’ordre variable : traces, éclatement, inégalités de Hardy. Séminaire EDP, École Polytechnique. (2006-2007) - Exp. XVII.
Code
23. N. Mihalache, F. Vigneron. GitHub project FastPolyEval, a Fast Polynomial Evaluator implementing our algorithm on rapid evaluation of polynomials of arbitrary high degree. See also the associated documentation and research article (item [20]).
Additional published works (books, videos, code...)
24. F. Vigneron. Création du parcours Apprendre Autrement en Licence de Sciences pour l’Ingénieur : le point de vue d’un mathématicien. (95 pages memoir, in French). Mention spéciale du Prix Jacqueline Ferrand 2018 (SMF).
25. F. Vigneron. Localisation et décroissance des champs en mécanique des fluides et des plasmas & Espaces fonctionnels associés à une famille de champs de vecteurs. (178 pages, in French). PhD thesis, defended on November 22, 2006 at École Polytechnique.
26. F. Vigneron. Contributions à l’étude des fondements de l’hydrodynamique, à l’analyse des EDP, à l’analyse multi-fractale, à l’analyse sous-riemannienne et à la pédagogie des mathématiques. (107 pages, in French). Habilitation Thesis (HDR), defended on November 22, 2018 at Université Paris-Est, Créteil.
27. F. Vigneron. My YouTube channel which includes 25 animations vidéos (13 min) associated to the paper [10] on Fourier analysis and 2 videos (40 min) of presentation of my HdR.
Slides & posters
This section contains a few slides of my talks.
PDEs, hydrodynamics & analysis
Introduction to 3D Hydrodynamic turbulence (from [6]; University of Illinois, Chicago, 2013).
Global well-posedness of a non-local Burgers equation (from [8]; SIAM, Phoenix, AZ, 2015).
Freezing the non-local Burgers equation (from [8] and prospective numerical simulations; Mathflows, Bedlewo, 2017).
Non-local models of fluid turbulence (poster from [8]; CIRM, Dec. 2018).
Realistic modeling of hydrodynamic turbulence (from [6], [8], [14] and current research; Reims, Lille, Feb. 2020).
On some properties of the Curl operator and their consequences for the Navier-Stokes System (Lyon, Fev. 2022; Evry, Reims, Mar. 2022).
Multifractal analysis on the Heisenberg group (from [9]; SCAM, Créteil, Nov. 2018).
Algorithms & HPC
How to split a tera-polynomial ? (from [22]; see also a video recording from JCAD2021).
A new algorithm for Fast Polynomial Evaluation (Journées Romeo 2022, 2023 & JCAD2023).
Fun with polynomials (Reims, 2023) containing a short ODE proof of the fundamental theorem of algebra.
Pedagogy
Le parcours Apprendre Autrement (from [12]; Congrès de la SMF, Lille, 2018; Sorbonne Université, 2018; Promosciences, Jan. 2019).
Bilan du parcours Apprendre Autrement (from [12]; Promosciences, Jan. 2020) with video testimonies of former students (testimony 1, testimony 2).
Habilitation thesis
F. Vigneron. Contributions à l’étude des fondements de l’hydrodynamique, à l’analyse des EDP, à l’analyse multi-fractale, à l’analyse sous-riemannienne et à la pédagogie des mathématiques. (107 pages, in French). Habilitation Thesis (HDR), defended on November 22, 2018 at Université Paris-Est, Créteil.
Reports on my HDR, written by J.L. Bona (University of Illionois, Chicago), J.-M. Coron (Sorbonne Université) and F. Sueur (Université de Bordeaux).
Jury signatures and defense report by H. Bahouri, J.L.Bona, J.-Y. Chemin, J.-M. Coron, A.-L. Dalibard, I. Gallagher, T. Gallay, C. Guillopé, F. Sueur.
My HDR Diploma.
Printable slides of the defense.
Video recording of my HDR defense (40 min) on my channel.
Live experiment during my HDR defense (1 min 38, no sound).
PhD thesis
F. Vigneron. Localisation et décroissance des champs en mécanique des fluides et des plasmas & Espaces fonctionnels associés à une famille de champs de vecteurs. (178 pages, in French). PhD thesis, defended on November 22, 2006 at École Polytechnique.
Reports on my PhD by J.-Y. Chemin (adviser, Sorbonne Université), G. David (Université d'Orsay), V. Sverak (University of Minnesota).
Jury signatures and defense report by C.Bardos, J.-M.Bony, J.-Y. Chemin, G. David, H. Pajot and V. Sverak.
My PhD Diploma.
Printable slides of the defense.
