Christophe Prange

Announcements

Ph.D. Students and Postdocs

Preprints and Publications

• Unified quantitative analysis of the Stokes equations in dilute perforated domains via layer potentials
  (with Wenjia Jing and Yong Lu) Submitted (2024)
  arXiv
• Free boundary regularity of vacuum states for incompressible viscous flows in unbounded domains
  (with Jin Tan) Submitted (2023)
  arXiv
• Blow-up of dynamically restricted critical norms near a potential Navier-Stokes singularity
  (with Tobias Barker and Pedro Fernández-Dalgo) Mathematische Annalen, 389, 1517-1543, (2024)
  arXiv, journal
• On symmetry breaking for the Navier-Stokes equations
  (with Tobias Barker and Jin Tan) Comm. Math. Phys., 405(25), (2024)
  arXiv, journal
• Epsilon regularity for the Navier-Stokes equations via weak-strong uniqueness
  (with Dallas Albritton and Tobias Barker) J. Math. Fluid Mech., 25(49) (2023); special issue in the memory of Olga Ladyzhenskaya
  arXiv, journal
• From concentration to quantitative regularity: a short survey of recent developments for the Navier-Stokes equations
  (with Tobias Barker) Vietnam Journal of Mathematics (2023); special issue dedicated to Carlos Kenig's 70th birthday
  arXiv, journal
• Localized smoothing and concentration for the Navier-Stokes equations in the half space
  (with Dallas Albritton and Tobias Barker) Journal of Functional Analysis, 284(1) (2023)
  arXiv, journal
• Large-scale regularity for the stationary Navier-Stokes equations over non-Lipschitz boundaries
  (with Mitsuo Higaki and Jinping Zhuge) Analysis & PDE, 17(1), 171-242 (2024)
  arXiv, journal
• Motion of several slender rigid filaments in a Stokes flow
  (with Richard Höfer and Franck Sueur) Journal de l'École polytechnique -- Mathématiques, Tome 9, 327-380 (2022)
  arXiv, journal
• Mild criticality breaking for the Navier-Stokes equations
  (with Tobias Barker) J. Math. Fluid Mech., 23(66) (2021)
  arXiv, journal
• Anisotropy and stratification effects in the dynamics of fast rotating compressible fluids
  (with Edoardo Bocchi and Francesco Fanelli) Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire, 39(3), 647-704 (2022)
  arXiv, journal
• Quantitative regularity for the Navier-Stokes equations via spatial concentration
  (with Tobias Barker) Comm. Math. Phys., 385(2), 717-792 (2021)
  arXiv, journal
• Regularity for the stationary Navier-Stokes equations over bumpy boundaries and a local wall law
  (with Mitsuo Higaki) Calc. Var. Partial Differential Equations, 59, 131 (2020)
  arXiv, journal
• Scale-invariant estimates and vorticity alignment for Navier-Stokes in the half-space with no-slip boundary conditions
  (with Tobias Barker) Arch. Ration. Mech. Anal., 235(2), 881-926 (2020)
  arXiv, journal
• Localized smoothing for the Navier-Stokes equations and concentration of critical norms near singularities
  (with Tobias Barker) Arch. Ration. Mech. Anal., 236, 1487-1541 (2020)
  arXiv, journal
• On stability of blow-up solutions of the Burgers vortex type for the Navier-Stokes equations with a linear strain
  (with Yasunori Maekawa and Hideyuki Miura) J. Math. Fluid Mech., 21(4), 46 (2019)
  arXiv, journal
• Local energy weak solutions for the Navier-Stokes equations in the half-space
  (with Yasunori Maekawa and Hideyuki Miura) Comm. Math. Phys., 367(2), 517-580 (2019)
  arXiv, journal
• Estimates for the Navier-Stokes equations in the half-space for non localized data
  (with Yasunori Maekawa and Hideyuki Miura) Analysis & PDE, 13(4), 945-1010 (2020)
  arXiv, journal
• Quantitative analysis of boundary layers in periodic homogenization
  (with Scott Armstrong, Tuomo Kuusi and Jean-Christophe Mourrat) Arch. Ration. Mech. Anal., 226(2), 695-741 (2017)
  arXiv, journal
• Improved regularity in bumpy Lipschitz domains
  (with Carlos Kenig) J. Math. Pures Appl., 113, 1-36 (2018)
  arXiv, journal
• Uniform Lipschitz estimates in bumpy half-spaces
  (with Carlos Kenig) Arch. Ration. Mech. Anal., 216(3), 703-765 (2015)
  arXiv, journal
• Newtonian limit for weakly viscoelastic fluid flows
  (with Didier Bresch) SIAM J. Math. Anal., 46(2), 1116-1159 (2014)
  HAL, journal
• Well-posedness of the Stokes-Coriolis system in a half-space over a rough surface
  (with Anne-Laure Dalibard) Analysis & PDE, 7-6, 1253--1315 (2014)
  arXiv, journal
• Asymptotic analysis of boundary layer correctors in periodic homogenization
  SIAM J. Math. Anal., 45(1), 345-387 (2013)
  arXiv, journal
• First-order expansion for the Dirichlet eigenvalues of an elliptic system with oscillating coefficients
  Asymptotic Analysis, 83(3), 207-235 (2013)
  arXiv, journal

Proceedings

• Large-scale regularity for fluids over rough boundaries
  Oberwolfach Reports (2021)
  journal
• Infinite energy solutions to the Navier-Stokes equations in the half-space and applications
  Séminaire Laurent Schwartz-EDP et applications (2017-2018), Exp. No. 2, 18 p.
  arXiv, journal
• Uniform estimates in homogenization: compactness methods and applications
  Journées Equations aux Dérivées Partielles Exp. No. 7, 25 p. (2014)
  HAL, journal

Videos

Recent Talks

Teaching in 2024-2025

Previous Teaching

• Math 27300, Basic Theory of Ordinary Differential Equations (Winter 2015)
• Math 20000, Mathematical Methods for Physical Science 1 (Fall 2014)
• Math 20400, Analysis 2 (Fall 2014)
• Math 20100, Mathematical Methods for Physical Science 2 (Winter 2014)
• Math 20500, Analysis 3 (Winter 2014)
• Math 20000, Mathematical Methods for Physical Science 1 (Fall 2013)
• Math 20400, Analysis 2 (Fall 2013)