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Publications and preprints

2026Forward self-similar solutions to the 2D Navier--Stokes equations with Julien Guillod, Mikhail Korobkov, Xiao Ren arXiv preprint arXiv:2601.03161. Submitted to Advances in MatharXiv
2026Kinetic shock profiles for the Landau equation with Jacob Bedrossian, Matthew Novack Ars Inveniendi Analyticajournal
2025Sharp uniform-in-diffusivity mixing rates for passive scalars in parallel shear flows with Rajendra Beekie arXiv preprint arXiv:2511.18536. Submitted to Annals of PDEarXiv
2025Vanishing viscosity non-unique solutions to the forced 2D Euler equations with Maria Colombo, Giulia Mescolini arXiv preprint arXiv:2507.19257. Submitted to CPAMarXiv
2025Rods in flows: the PDE theory of immersed elastic filaments with Laurel Ohm arXiv preprint arXiv:2503.14440. Submitted to ARMAarXiv
2025Linear and nonlinear instability of vortex columns with Wojciech O\.za\'nski Journal of the European Mathematical Societyjournal arXiv
2024Instability and Non-uniqueness for the 2D Euler Equations, after M. Vishik: (AMS-219) with Elia Brué, Camillo De Lellis, Maria Colombo, Vikram Giri, Maximilian Janisch, Hyunju Kwonjournal arXiv
2024Variational methods for the kinetic Fokker–Planck equation with Scott Armstrong, Jean-Christophe Mourrat, Matthew Novack Analysis \& PDEjournal arXiv
2023Remarks on the complex Euler equations with W. Jacob Ogden Communications on Pure and Applied Analysisjournal arXiv
2023Sharp bounds on enstrophy growth for viscous scalar conservation laws with Nicola De Nitti Nonlinearityjournal arXiv
2023Epsilon regularity for the Navier-Stokes equations via weak-strong uniqueness with Tobias Barker, Christophe Prange J. Math. Fluid Mech.journal arXiv
2023Gluing non-unique Navier-Stokes solutions with Elia Brué, Maria Colombo Ann. PDEjournal arXiv
2023Non-uniqueness of Leray solutions to the hypodissipative Navier-Stokes equations in two dimensions with Maria Colombo Comm. Math. Phys.journal arXiv
2023On the stabilizing effect of swimming in an active suspension with Laurel Ohm SIAM J. Math. Anal.journal arXiv
2023Localized smoothing and concentration for the Navier-Stokes equations in the half space with Tobias Barker, Christophe Prange J. Funct. Anal.journal arXiv
2023Regularity properties of passive scalars with rough divergence-free drifts with Hongjie Dong Arch. Ration. Mech. Anal.journal arXiv
2022Non-uniqueness of Leray solutions of the forced Navier-Stokes equations with Elia Brué, Maria Colombo Annals of Mathematicsjournal arXiv
2022Enhanced dissipation and H\"ormander's hypoellipticity with Rajendra Beekie, Matthew Novack Journal of Functional Analysisjournal arXiv
2022Remarks on sparseness and regularity of Navier--Stokes solutions with Zachary Bradshaw Nonlinearityjournal arXiv
2022Long-time behavior of scalar conservation laws with critical dissipation with Rajendra Beekie Annales de l'Institut Henri Poincar\'e C, Analyse non lin\'eairejournal arXiv
2021Non-decaying solutions to the critical surface quasi-geostrophic equations with symmetries with Zachary Bradshaw Transactions of the American Mathematical Societyjournal arXiv
2020Localised necessary conditions for singularity formation in the Navier-Stokes equations with curved boundary with Tobias Barker Journal of Differential Equationsjournal arXiv
2019On local Type I singularities of the Navier-Stokes equations and Liouville theorems with Tobias Barker J. Math. Fluid Mech.journal arXiv
2019Global weak Besov solutions of the Navier-Stokes equations and applications with Tobias Barker Arch. Ration. Mech. Anal.journal arXiv
2018Blow-up criteria for the Navier--Stokes equations in non-endpoint critical Besov spaces Anal. PDEjournal arXiv