Publications

Center for AI Safety, HLE Contributors Consortium, Scale AI. A benchmark of expert-level academic questions to assess AI capabilities. Nature 649, 1139-1146, 2026.
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Dallas Albritton, Julien Guillod, Mikhail Korobkov, Xiao Ren. Forward self-similar solutions to the 2D Navier–Stokes equations. 2026.
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Anne-Laure Dalibard, Julien Guillod, Antoine Leblond. Long-time behavior of the Stokes-transport system in a channel. Analysis & PDE 18, 1955–2032, 2025.
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Bernard Di Martino, Chourouk El Hassanieh, Edwige Godlewski, Julien Guillod, Jacques Sainte-Marie. Hyperbolicity of a semi-Lagrangian formulation of the hydrostatic free-surface Euler system. Nonlinearity 38, 015018, 2025.
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Julien Guillod. Python Programming for Mathematics. Chapman & Hall/CRC, The Python Series, 2025.
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Julien Guillod. Programmation Python par la pratique - 2e édition. Dunod, Sciences Sup, 2024.
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Julien Guillod, Vladimír Šverák. Numerical investigations of non-uniqueness for the Navier–Stokes initial value problem in borderline spaces. Journal of Mathematical Fluid Mechanics volume 25, 46., 2023.
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Julien Guillod, Mikhail Korobkov, Xiao Ren. Existence and uniqueness for plane stationary Navier–Stokes flows with compactly supported force. Communications in Mathematical Physics 397, 729-762., 2022.
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Julien Guillod. Programmation Python par la pratique. Dunod, Sciences Sup, 2021.
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Julien Guillod, Guido Schneider, Peter Wittwer, Dominik Zimmermann. Nonlinear stability at the Eckhaus boundary. SIAM Journal on Mathematical Analysis, 2018.
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Julien Guillod, Peter Wittwer. Existence and uniqueness of steady weak solutions to the Navier–Stokes equations in $\mathbb{R}^2$. Proceedings of the American Mathematical Society, 2018.
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Julien Guillod, Peter Wittwer. Optimal asymptotic behavior of the vorticity of a viscous flow past a two-dimensional body. Journal de Mathématiques Pures et Appliquées, 2017.
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Julien Guillod. On the asymptotic stability of steady flows with nonzero flux in two-dimensional exterior domains. Communications in Mathematical Physics, 2017.
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Julien Guillod, Peter Wittwer. On the stationary Navier–Stokes equations in the half-plane. Annales Henri Poincaré, 2016.
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Julien Guillod. Steady solutions of the Navier–Stokes equations in the plane. arXiv, 2015.
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Julien Guillod, Peter Wittwer. Generalized scale-invariant solutions to the two-dimensional stationary Navier–Stokes equations. SIAM Journal on Mathematical Analysis, 2015.
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Julien Guillod, Peter Wittwer. Asymptotic behaviour of solutions to the stationary Navier–Stokes equations in two-dimensional exterior domains with zero velocity at infinity. Mathematical Models and Methods in Applied Sciences, 2015.
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Julien Guillod. On the stationary Navier–Stokes equations in two dimensions. PhD thesis, Université de Genève, 2015.