My research focuses on the mathematical modelling and analysis of media in which motion is limited by density, contact or saturation. My work connects modelling, PDE analysis and numerical approximation.
Research interests
Density saturation
In granular media, concentrated suspensions and crowds, packing constraints limit the density of the medium. How can we describe the coexistence of free and congested regions? I study models that account for this constraint and the dynamics of the interfaces between these regions.
From microscopic contact to collective dynamics
In a suspension, lubrication, contact and collisions influence particle motion. How do these interactions translate to larger scales? I work on the development and mathematical justification of continuum
models from particle systems.
Transitions and front propagation
How do congested regions form and recede? I study these transitions and the propagation of the associated fronts, as well as numerical approximations designed to capture them.
Derivation of the one-dimensional Euler equations with a congestion constraint as the hydrodynamic limit of a particle system with inelastic collisions.
All publications and preprints →
Preprints
A. Lefebvre-Lepot, M.A. Mehmood, C. Perrin, E. Zatorska. «Microscopic derivation of a one-dimensional lubrication model including rough repulsive layers» preprint HAL
C. Perrin «Microscopic derivation of the one-dimensional constrained Euler equations» preprint HAL
Complete list
N. Chaudhuri, M. A. Mehmood, C. Perrin, E. Zatorska. «Duality solutions to the hard-congestion model for the dissipative Aw-Rascle system»
Communications in Partial Differential Equations, vol. 49, no. 7-8, pp. 671--697, 2024 (preprint available on HAL )
A.-L. Dalibard, C. Perrin. «Local and global well-posedness of one-dimensional free-congested equations»
Annales Henri Lebesgue, vol. 7, pp. 1175-1243, 2024 (preprint available on HAL )
N. Chaudhuri, L. Navoret, C. Perrin, E. Zatorska. «Hard congestion limit in a dissipative Aw-Rascle system»
Nonlinearity, vol. 37, 45018, 2024 (preprint available on HAL )
F. Ancona, R. Bianchini, C. Perrin. «Hard congestion limit of the p-system in the BV setting» ESAIM: Proceedings and Surveys , vol. 72, pp. 41–63, 2023
(preprint available on HAL )
C. Burtea, S. Gavrilyuk, C. Perrin. «Hamilton's principle of stationary action in multiphase flow modeling»
Lecture notes - Panoramas et Synthèses (preprint available on HAL )
A.-L. Dalibard, G. Lopez-Ruiz, C. Perrin. «Traveling waves for the porous medium equation in the incompressible limit: asymptotic behavior and nonlinear stability»
Indiana University Mathematics Journal, vol. 73, no. 2, pp 681-643 (preprint available on HAL )
C. Perrin, K. Saleh. «Numerical staggered schemes for the free-congested Navier-Stokes equations»
SIAM Journal on Numerical Analysis 60.4 (2022): 1824-1852 (preprint available on HAL )
A.-L. Dalibard, C. Perrin. «Partially congested propagation fronts in one-dimensional Navier-Stokes equations»
Journal of Elliptic and Parabolic Equations 7.2 (2021): 491-507 (preprint available on HAL )
R. Bianchini, C. Perrin. «Soft congestion approximation to the one-dimensional constrained Euler equations»
Nonlinearity, vol. 34, no. 10, p. 6910, 2021 (preprint available on HAL )
C. Perrin. «A remark on memory effects in constrained fluid systems» Proceeding «Workshop on Compressible Multiphase Flows» 2019, ESAIM: Proceedings and Surveys, December 2020, vol. 69, p. 56-69 (2020) ( HAL )
A.-L. Dalibard, C. Perrin. «Existence and stability of partially congested propagation fronts in a one-dimensional Navier-Stokes model» Communications in Mathematical Sciences, Vol. 18, n.7, p.1775-1813 (2020) ( HAL )
C. Perrin, K. Saleh. «A convergent FV - FE scheme for the stationary compressible Navier-Stokes equations» IMA Journal of Numerical Analysis, 2021, vol. 41, no 2, p. 826-899 ( HAL , version longue disponible )
D. Bresch, S. Necasova, C. Perrin. «Compression effects in heterogeneous media» Journal de l'École Polytechnique - Mathématiques Tome 6 (2019), p. 433-467 (updated version on HAL )
C. Perrin. «An overview on congestion phenomena in fluid equations» Proceeding Journées EDP 2018 ( HAL )
C. Perrin, M. Westdickenberg. «One-dimensional granular system with memory effects» SIAM Journal of Mathematical Analysis, vol. 50(6), p.5921-5946, 2018 ( HAL )
C. Perrin. «Modelling of phase transitions in one-dimensional granular flows»
ESAIM: Proceedings and Surveys, vol. 58, p. 78-97 (2017).
M. Fabre, S. Faure, M. Laurière, B. Maury, C. Perrin. «Non classical solution of a conservation law arising in vehicular traffic»
ESAIM: Proceedings and Surveys, vol. 55, p. 131-147 (2016).
C. Perrin. «Pressure Dependent Viscosity Model for Granular Media Obtained from Compressible Navier-Stokes Equations»
Appl Math Res Express, vol. 2016, Iss. 2, p. 289-333 (2016)
C. Perrin, E. Zatorska. «Free/Congested Two-Phase Model from Weak Solutions to Multi-Dimensional Compressible Navier-Stokes Equations»
Communications in Partial Differential Equations, vol. 40, Iss. 8, p. 1558-1589 (2015)
D. Bresch, C. Perrin, E. Zatorska. «A singular Limit of Navier-Stokes System Leading to a Free/Congested zones Two-Phase Model». C. R. Acad. Sci. Paris.,vol. 352, Iss. 9 p. 685--690 (2014)
For a full overview of my activities (talks, teaching, administrative/editorial responsibilities, science communication and outreach) please see my CV.
