My research focuses on certain Partial Differential Equations used in fluid mechanics. I study the qualitative behavior of solutions, their existence and uniqueness or their stability, with harmonic analysis methods.
Especially, I'm interested in the following topics: mathematical magnetohydrodynamics, incompressible fluids, certain singular perturbation problems and Littlewood-Paley analysis.
- With Martin Donati and Ludovic Godard-Cadillac,
Existence and Uniqueness for the SQG Vortex-Wave System when the Vorticity is Constant near the Point-Vortex,
arXiv:2401.02728v1 (submitted), 2024. arXiv version. - With Geoffrey Lacour,
Weak Solutions for a non-Newtonian Stokes-Transport System,
arXiv:2401.02599v1 (submitted), 2024. arXiv version. - On the Well-Posedness of a Fractional Stokes-Transport System,
arXiv:2301.10511v1 (submitted), 2023. arXiv version. - Remarks on Chemin's space of homogeneous distributions,
Math. Nachr. 00 (2023), 1-19. Link to the journal. arXiv version. - Bounded solutions in incompressible hydrodynamics,
J. Funct. Anal., Vol. 286, 5, 2024, 110290. Link to the journal. arXiv version. - With Francesco Fanelli,
Symmetry breaking in ideal magnetohydrodynamics: the role of the velocity,
J. Elliptic Parabol. Equ. (2021). Link to the journal. arXiv version. - With Francesco Fanelli,
Elsässer formulation of the ideal MHD and improved lifespan in two space dimensions,
J. Math. Pures Appl. (9) 169 (2023), pp. 189-236. Link to the journal. arXiv version. - With Francesco Fanelli,
Rigorous derivation and well-posedness of a quasi-homogeneous ideal MHD system,
Nonlinear Anal. Real World Appl. 60 (2021), 103284. Link to the journal. arXiv version. - With Francesco Fanelli,
On the fast rotation asymptotics of a non-homogeneous incompressible MHD system,
Nonlinearity 34. n. 4 (2021), 2483. Link to the journal. arXiv verison.
PhD Dissertation
My PhD dissertation (written in English), defended in June 2022, is about the Mathematical Study of Fluids Interacting with a Magnetic Field and can be downloaded here.