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Francesco Fanelli

Research

Research informations

Research interests
  • PDEs of fluid dynamics: inviscid fluids, variable density, incompressible and compressible fluids, capillarity effects, geophysical fluids, MHD system.

  • Singular perturbation problems, asymptotic behaviour: fast rotation limit, incompressible limit, long-time dynamics, multi-scale limits.

  • Hyperbolic operators with low regularity coefficients (second-order equations, first-order systems): well-posedness, control and optimal control.

  • Fourier Analysis methods for PDEs, Littlewood-Paley theory and paradifferential calculus (classical and with parameters), Besov spaces.

  • Harmonic Analysis tools: oscillatory integrals, singluar integrals.
Publications         Publications available on   arXiv     -     Profile on   Google Scholar     -     Profile on   ResearchGate

Published or accepted papers


Submitted papers


Proceedings


Dissertations

Published or accepted papers
  1. "Effective velocity and L∞-based well-posedness for incompressible fluids with odd viscosity"
    (with Alexis F. Vasseur)
    SIAM Journal on Mathematical Analysis, accepted for publication, 2024

  2. "Well-posedness results for hyperbolic operators with coefficients rapidly oscillating in time"
    (with Ferruccio Colombini and Daniele Del Santo)
    Annali della Scuola Normale Superiore Classe di Scienze, accepted for publication, 2023

  3. "Well-posedness and singularity formation for the Kolmogorov two-equation model of turbulence in 1-D"
    (with Rafael Granero-Belinchón)
    Journal of Dynamics and Differential Equations, accepted for publication, 2023

  4. "Thermally driven fluid convection in the incompressible limit regime"
    (with Eduard Feireisl)
    Pure and Applied Analysis, 6(3), 2024

  5. "Well-posedness theory for non-homogeneous incompressible fluids with odd viscosity"
    (with Rafael Granero-Belinchón and Stefano Scrobogna)
    Journal de Mathématiques Pures et Appliquées (9), 187, 2024

  6. "Well-posedness of the Kolmogorov two-equation model of turbulence in optimal Sobolev spaces"
    (with Ophélie Cuvillier and Elena Salguero)
    Journal of Evolution Equations, 23(4), 2023

  7. "Fast rotating non-homogeneous fluids in thin domains and the Ekman pumping effect"
    (with Marco Bravin)
    Journal of Mathematical Fluid Mechanics, 25(4), 2023

  8. "Low Mach number limit for degenerate Navier-Stokes equations in presence of strong stratification"
    (with Ewelina Zatorska)
    Communications in Mathematical Physics, 400(3), 2023

  9. "Elsässer formulation of the ideal MHD and improved lifespan in two space dimensions"
    (with Dimitri Cobb)
    Journal de Mathématiques Pures et Appliquées (9) , 189, 2023

  10. "Finite time blow-up for some parabolic systems arising in turbulence theory"
    (with Rafael Granero-Belinchón)
    Zeitschrift für Angewandte Mathematik und Physik, 73(5), 2022

  11. "Anisotropy and stratification effects in the dynamics of fast rotating compressible fluids"
    (with Edoardo Bocchi and Christophe Prange)
    Annales de l'Institut Henri Poincaré C Analyse Non Linéaire, 39(3), 2022

  12. "Incompressible and fast rotation limit for barotropic Navier-Stokes equations at large Mach numbers"
    Physica D, 428, 2021

  13. "A numerical investigation of Brockett's ensemble optimal control problems"
    (with Jan Bartsch, Alfio Borzì and Souvik Roy)
    Numerische Mathematik, 149(1), 2021

  14. "Ergodic theory for energetically open compressible fluid flows"
    (with Eduard Feireisl and Martina Hofmanová)
    Physica D, 423, 2021

  15. "On the fast rotation asymptotics of a non-homogeneous incompressible MHD system"
    (with Dimitri Cobb)
    Nonlinearity, 34(4), 2021

  16. "A multi-scale problem for viscous heat-conducting fluids in fast rotation"
    (with Daniele Del Santo, Gabriele Sbaiz and Aneta Wróblewska-Kamińska)
    Journal of Nonlinear Science, 31(1), 2021

  17. "Some remarks on steady solutions to the Euler system in ℝd"
    (with Eduard Feireisl)
    Applied Mathematics Letters, 116, 2021

  18. "Rigorous derivation and well-posedness of a quasi-homogeneous ideal MHD system"
    (with Dimitri Cobb)
    Nonlinear Analysis: Real World Applications, 60, 2021

  19. "Statistical solutions to the barotropic Navier-Stokes system"
    (with Eduard Feireisl)
    Journal of Statistical Physics, 181(1), 2020

  20. "On the Cauchy problem for microlocally symmetrizable hyperbolic systems with log-Lipschitz coefficients"
    (with Ferruccio Colombini, Daniele Del Santo and Guy Métivier)
    Indiana University Mathematics Journal, 69(3), 2020

  21. "A well-posedness result for viscous compressible fluids with only bounded density"
    (with Raphaël Danchin and Marius Paicu)
    Analysis & PDE, 13(1), 2020

  22. "Asymptotics of fast rotating density-dependent incompressible fluids in two space dimensions"
    (with Isabelle Gallagher)
    Revista Matemática Iberoamericana, 35(6), 2019

  23. "A theoretical investigation of Brockett's ensemble optimal control problems"
    (with Jan Bartsch, Alfio Borzì and Souvik Roy)
    Calculus of Variations and Partial Differential Equations, 58(5), 2019

  24. "Global well-posedness and long-time dynamics for a higher order Quasi-Geostrophic type equation"
    (with Francesco De Anna)
    Journal of Functional Analysis, 274(8), 2018

  25. "Corrigendum to «Highly rotating viscous compressible fluids in presence of capillarity effects»"
    Mathematische Annalen, 370(3-4), 2018

  26. "Some local questions for hyperbolic systems with non-regular time dependent coefficients"
    Journal of Hyperbolic Differential Equations, 14(2), 2017

  27. "A singular limit problem for rotating capillary fluids with variable rotation axis"
    Journal of Mathematical Fluid Mechanics, 18(4), 2016

  28. "Highly rotating viscous compressible fluids in presence of capillarity effects"
    Mathematische Annalen, 366(3-4), 2016

  29. "The well-posedness issue in Sobolev spaces for hyperbolic systems with Zygmund-type coefficients"
    (with Ferruccio Colombini, Daniele Del Santo and Guy Métivier)
    Communications in Partial Differential Equations, 40(11), 2015

  30. "Analysis of an inviscid zero-Mach number system in endpoint Besov spaces for finite-energy initial data"
    (with Xian Liao)
    Journal of Differential Equations, 259(10), 2015

  31. "The well-posedness issue for an inviscid zero-Mach number system in general Besov spaces"
    (with Xian Liao)
    Asymptotic Analysis, 93(1-2), 2015

  32. "Weak observability estimates for 1-D wave equations with rough coefficients"
    (with Enrique Zuazua)
    Annales de l'Institut Henri Poincaré C Analyse Non Linéaire, 32(2), 2015

  33. "A well-posedness result for hyperbolic operators with Zygmund coefficients"
    (with Ferruccio Colombini, Daniele Del Santo and Guy Mévier)
    Journal de Mathématiques Pures et Appliquées (9) , 100(4), 2013

  34. "Time-dependent loss of derivatives for hyperbolic operators with non-regular coefficients"
    (with Ferruccio Colombini, Daniele Del Santo and Guy Métivier)
    Communications in Partial Differential Equations, 38(10), 2013

  35. "Conservation of geometric structures for non-homogeneous inviscid incompressible fluids"
    Communications in Partial Differential Equations , 37(9), 2012

  36. "The well-posedness issue for the density-dependent Euler equations in endpoint Besov spaces"
    (with Raphaël Danchin)
    Journal de Mathématiques Pures et Appliquées (9), 96(3), 2011

  37. "A note on non-homogeneous hyperbolic operators with low regularity coefficients"
    (with Ferruccio Colombini)
    Rendiconti dell'Istituto di Matematica dell'Università di Trieste , vol. 42 suppl., 2010

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Submitted papers
  1. "Ekman boundary layers in a domain with topography"
    (with Jean-Yves Chemin and Isabelle Gallagher)
    submitted, 2024

  2. "Global existence for non-homogeneous incompressible inviscid fluids in presence of Ekman pumping"
    (with Marco Bravin)
    submitted, 2024

  3. "Geophysical flows and the effects of a strong surface tension"
    submitted, 2016

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Proceedings of conferences and seminars
  1. "On the influence of gravity in the dynamics of geophysical flows"
    (with Daniele Del Santo, Gabriele Sbaiz and Aneta Wróblewska-Kamińska)
    Mathematics in Engineering, 5(1), 2023

  2. "Simmetry breaking in ideal magnetohydrodynamics: the role of the velocity"
    (with Dimitri Cobb)
    Journal of Elliptic and Parabolic Equations, 7(2), 2021

  3. "No loss of derivatives for hyperbolic operators with Zygmund-continuous coefficients in time"
    (with Ferruccio Colombini and Daniele Del Santo)
    "Anomalies in Partial Differential Equations", Springer-INdAM series, Springer, 2021

  4. "A few remarks on hyperbolic systems with Zygmund in time coefficients"
    "Shocks, singularities and oscillations in Nonlinear Optics and Fluid Mechanics", Springer-INdAM series, Springer, 2017

  5. "A note on viscous capillary fluids in fast rotation"
    Bruno Pini Mathematical Analysis Seminar, Univ. Bologna, 2015

  6. "A note on complete hyperbolic operators with log-Zygmund coefficients"
    (with Ferruccio Colombini, Daniele Del Santo and Guy Mévier)
    "Fourier Analysis", Trends in Mathematics, Birkhäuser/Springer, 2014

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Dissertations
  • "Heterogeneity and low regularity issues in PDEs arising from Fluid Mechanics" pdf button
    Habilitation thesis (30/05/2023)
    Université Claude Bernard Lyon 1
    Referees: Anne-Laure Dalibard, David Lannes, Nader Masmoudi
    Other members of the Defence Commettee: Thomas Alazard, Jean-Yves Chemin, Raphaël Danchin, Isabelle Gallagher,
                                                                          Dragoş Iftimite, Anna Laura Mazzucato, Laure Saint-Raymond

  • "Mathematical analysis of models of non-homogeneous fluids and of hyperbolic equations with low regularity coefficients" pdf button
    Ph.D. thesis (28/05/2012)
    Scuola Internazionale Superiore di Studi Avanzati & Université Paris Est, École Doctorale MSTIC
    (supported also by the "Vinci 2010" fellowship of the Università Italo-Francese / Université Franco-Italienne)
    Supervisors: Prof. Ferruccio Colombini, Prof. Raphaël Danchin, Prof. Andrei Agrachev
    Referees: Prof. Isabelle Gallagher, Prof. Nicolas Lerner
    Other members of the Defence Commettee: Prof. Stefano Bianchini, Prof. Marco Cannone, Prof. Gianni Dal Maso

  • "Para-differential calculus and its applications to hyperbolic problems"
    Master thesis (22/10/2008) - Supervisor: Prof. Ferruccio Colombini
    Università degli Studi di Trieste & Scuola Internazionale Superiore di Studi Avanzati

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