Research

I am specialized in the analysis of partial differential equations as well as calculus of variations.

My main research activities focus on:

The rearrangements theory and construction of asymetric rearrangements.
The study of steady whirlpools geometric properties.
The dynamics of the points-vortex systems and the study of collapses.
The Vortex-Wave system for quasi-geostrophic flows.
The Study of electronic interaction between plasma and métal in the stationnary regime.
The minimizing configurations for the magnetic nano-particules and nano-filaments.

Publications et Preprints :

R. Côte, C. Courtès, G. Ferriere, L. Godard-Cadillac, Y. Privat, The Spear and the Ring: Emergent Structures in Magnetic Colloidal Suspensions, preprint (lire en PDF).

R. Côte, C. Courtès, G. Ferriere, L. Godard-Cadillac, Y. Privat, Existence and Uniqueness of Domain Walls for Notched Ferromagnetic Nanowires, preprint (read as PDF).

D. Cobb, M. Donati, L. Godard-Cadillac, Existence and Uniqueness for the SQG Vortex-Wave System when the Vorticity is Constant near the Point-Vortex, SIAM Journal for Mathematical Analysis, 2025 (read as PDF).

M. Donati, L. Godard-Cadillac, D. Iftimie, On the Dynamics of Point-Vortices with Positive Intensities collapsing with the boundary, Physica D: Nonlinear Phenomena, 2024, 470(A): 134402 (read as PDF).

M. Badsi, L. Godard-Cadillac, Variational radial sheath solutions for a kinetic model of a cylindrical Langmuir probe, Mathematical Methods in the Applied Sciences, 2024, 47(4): 1973-1993 (read as PDF).

M. Badsi, A. Crestetto, L. Godard-Cadillac, Variational radial solutions and numerical simulations for a kinetic model of a cylindrical Langmuir probe (read as PDF).

M. Donati, L. Godard-Cadillac, Hölder regularity for collapses of point-vortices, Nonlinearity, 2023, 36(11):5773 (read as PDF).

M. Badsi, L. Godard-Cadillac, Existence of solutions for a bi-species kinetic model of a cylindrical Langmuir probe, International Press of Boston, 2023, 21(4): 1097-1134 (read as PDF).

L. Godard-Cadillac, Hölder estimate for the 3 point-vortex problem with alpha-models, Comptes Rendus. Mathématique, 2023, 361(G1): 355-362 (read as PDF).

L. Godard-Cadillac, P. Gravejat, D. Smets, Co-rotating vortices with N fold symmetry for the inviscid surface quasi-geostrophic equation, Indiana Univ. Math. J., 2023, 72: 603-650 (read as PDF).

L. Godard-Cadillac, Vortex collapses for the Euler and Quasi-Geostrophic models. Discrete and Continuous Dynamical Systems, 2022, 42(7): 3143-3168 (read as PDF).

M. Badsi, M. Campos-Pinto, B. Després, L. Godard-Cadillac, A variational sheath model for stationary gyrokinetic Vlasov–Poisson equations, ESAIM. Mathematical modelling and numerical analysis, 2021, 55 (6): 2609-2642 (read as PDF).

L. Godard-Cadillac, Tamped functions: A rearrangement in dimension 1, Nonlinear Analysis, 2021, 209: 112354 (read as PDF).

L. Godard-Cadillac, Smooth traveling-wave solutions to the inviscid surface quasi-geostrophic equations. Comptes Rendus. Mathématique, 2021, 359(1): 85-98 (read as PDF).

L. Godard-Cadillac, Les vortex quasi-géostrophiques et leur désingularisation, PhD thesis, 2020, Sorbonne Université (read as PDF).

Gallery

Dynamics of points-vortices

Dynamics generated by a large number of vortices randomly chosen.

Nano-particles magnetism

Magnetic nano-particles system within a fluid and an external magnetic field.

Electronic flux at the interface between plasma and metal

Electron du plasma absorbé par la sonde métallique

An electron from the plasma is absorbed by the Langmuir probe at the center..

Biography

I am Ludovic Godard-Cadillac and I am associated professor for mathematics since Septembre 2023 at Bordeaux-INP and I teach at ENSEIRB-MATMECA.

I do my research activities at the Institut de Mathématiques de Bordeaux and I am specialized in the domain of analysis for differential equations and partial differential equations and also their use in the domain of calculus of variations.

A brief resume :

Since sept. 2023 : Associate professor for Mathematics at Bordeaux-INP.
2022 - 2023 : Post-Doctorante at Institut de Recherche Mathématique Avancée (Strasbourg) with Raphaël Côte and Yannick Privat.
2021 - 2022 : Post-Doctorante at Laboratoire de Mathématiques Jean Leray (Nantes) with Mehdi Badsi.
2020 - 2021 : Post-Doctorante at Dipartimento di Matematica Giuseppe Peano (Turin) with Susanna Terracini.
2017 - 2020 : PhD thesis in Mathematics at Laboratoire Jacques Louis Lions (Paris 6) under the supervision of Didier Smets and Philippe Gravejat.
2017 : End of studies dissertation at Institut de Recherche en Mathématiques de Rennes (Rennes) with Roger Lewandowsky.
2016 - 2017 : Master studies on PDE and numerical analysis (Paris 6).
2016 : Engineering internship at 44Screens and Computer Vision Center (Barcelone).
2015 : Engineering internship in Data sciences for plasma physics at Saint-Gobain Recherche (Aubervilliers).
2014 : Engineering internship in experimental ferromagnétism at CEA (Saclay).
2013 - 2015 : Student in engineering at Ecole Nationale des Ponts et Chaussées (Champs-sur-Marne).
2011 - 2013 : Studies in Mathematics and Physics at Lycée Joseph Joffre (Montpellier).

Research

Publications et Preprints :

Gallery

Biography

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