Research Interest
I am interested in the analysis of partial differential equations, particularly at the intersection of kinetic theory and fluid mechanics. My research primarily focuses on fractional diffusion limits for kinetic equations with heavy-tailed equilibria characterized by polynomial decay, falling within the framework of hydrodynamic limits. Additionally, I study the propagation of high regularity, such as Gevrey-type regularity or analyticity of solutions of fluid-kinetic systems, such as the Vlasov–Navier–Stokes system. I am also interested in broader questions concerning fluid-kinetic systems, particularly regarding existence, uniqueness, and qualitative properties such as long-time behavior of solutions, hydrodynamic limits and the (in)stability of equilibria.
I remain open to exploring other equations and expanding my research into new areas within kinetic theory, fluid mechanics, and partial differential equations in general.
Preprints (available on the arXiv)
- On the fractional diffusion for the linear Boltzmann equation with drift and general cross-section. 23 pages, arXiv:2503.09589, 2025, submitted.
Publications
- On the spectral problem and fractional diffusion limit for Fokker–Planck with/without drift and for a general heavy tail equilibrium. Journal of Differential Equations 455 (2026), 113971. (arXiv version, arXiv:2503.09589). https://doi.org/10.1016/j.jde.2025.113971.
- Gevrey regularity and analyticity for the solutions of the Vlasov–Navier–Stokes system. SIAM Journal on Mathematical Analysis (2024) 56:6, 7903–7939. arXiv:2310.14273.
- Fractional diffusion for Fokker–Planck equation with heavy tail equilibrium: An à la Koch spectral method in any dimension. Asymptot. Anal. 136 (2024), no. 2, 79–132. arXiv:2303.07162, with M. Puel.
- Construction of an eigen-solution for the Fokker–Planck operator with heavy tail equilibrium: an à la Koch method in dimension 1. 38 pages, arXiv:2303.07159, 2023, with M. Puel. To appear in Annales de la Faculté des Sciences de Toulouse.