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About Me
About Me
I am an Assistant Professor at the University of Wisconsin-Madison. My research interests are in pure and applied aspects of partial differential equations and fluid dynamics.
In 2022-23, I was an NSF Postdoctoral Fellow at Princeton University, where my sponsor was Peter Constantin. In 2021-22, I was a Member of the Institute for Advanced Study, where my mentor was Camillo De Lellis. In 2020-21, I was an NSF Postdoctoral Fellow at the Courant Institute at NYU, where my sponsor was Vlad Vicol. In 2020, I completed my PhD in Mathematics at the University of Minnesota under the supervision of Vladimír Šverák.
I am partially supported by an NSF Standard Grant.
Contact Information
Contact Information
Email: dalbritton [AT] wisc [DOT] edu
Office: Van Vleck 323
Weekly Schedule
Weekly Schedule
MWF 12:05-12:55 pm Partial Differential Equations (Math 719)
Office Hours: WF 11 am-12pm
M 3:30 pm PDE & Geometric Analysis Seminar
W 4 pm Physical Applied Mathematics Seminar (PhAM)
F 4 pm Colloquium
Red Rock Canyon, Nevada
Workshop on Kinetic Theory and Fluids
Workshop on Kinetic Theory and Fluids
Chanwoo Kim and I are co-organizing a workshop at the University of Wisconsin-Madison, March 28-30, 2025.
Information for Students
Information for Students
I am currently accepting PhD students. To work with me, you should already be enrolled in the PhD program at the University of Wisconsin-Madison. To determine whether we would work well together, a good start would be to do a reading course with me.
Research
Research
Papers
Papers
Non-unique vanishing viscosity solutions to the forced 2D Euler equations (with M. Colombo and G. Mescolini).
Rods in flows: the PDE theory of immersed elastic filaments (with L. Ohm). [arXiv]
Kinetic shock profiles for the Landau equation (with J. Bedrossian and M. Novack). [arXiv]
Linear and nonlinear instability of vortex columns (with W. Ozanski). [arXiv]
Sharp bounds on enstrophy growth for viscous scalar conservation laws (with N. De Nitti). Nonlinearity. [arXiv]
Remarks on the complex Euler equations (with J. Ogden). CPAA. [arXiv]
Epsilon regularity for the Navier-Stokes equations via weak-strong uniqueness (with T. Barker and C. Prange). J. Math. Fluid Mech. [arXiv]
Gluing non-unique Navier-Stokes solutions (with E. Brué and M. Colombo). Annals of PDE. [arXiv]
Non-uniqueness of Leray solutions to the hypodissipative Navier-Stokes equations in two dimensions (with M. Colombo). Communications in Mathematical Physics. [arXiv]
On the stabilizing effect of swimming in an active suspension (with L. Ohm). SIMA. [arXiv]
Localized smoothing and concentration for the Navier-Stokes equations in the half space (with T. Barker and C. Prange). J. Funct. Anal. [arXiv]
Non-uniqueness of Leray solutions of the forced Navier-Stokes equations (with E. Brué and M. Colombo). Annals of Mathematics, 2022. [arXiv] [Journal]
Variational methods for the kinetic Fokker-Planck equation (with S. Armstrong, J.-C. Mourrat, and M. Novack). Anal. PDE. [arXiv]
Remarks on sparseness and regularity of Navier-Stokes solutions (with Z. Bradshaw). Nonlinearity, 2022. [arXiv]
Regularity properties of passive scalars with rough divergence-free drifts (with H. Dong). ARMA. [arXiv]
Enhanced dissipation and Hörmander's hypoellipticity (with R. Beekie and M. Novack). J. Funct. Anal., 2022. [arXiv]
Non-decaying solutions to the critical surface quasi-geostrophic equations with symmetries (with Z. Bradshaw). Trans. Amer. Math. Soc., 2022. [arXiv] [Journal]
Long-time behavior of scalar conservation laws with critical dissipation (with R. Beekie). AIHP-AN, 2022. [arXiv]
Localised necessary conditions for singularity formation in the Navier-Stokes equations with curved boundary (with T. Barker). J. Differential Equations, 2020. [arXiv] [Journal]
On local Type I singularities of the Navier-Stokes equations and Liouville theorems (with T. Barker). J. Math. Fluid Mech., 2019. [arXiv] [Journal]
Global weak Besov solutions of the Navier-Stokes equations and applications (with T. Barker). Arch. Rational Mech. Anal., 2019. [arXiv] [Journal]
Blow-up criteria for the Navier-Stokes equations in non-endpoint critical Besov spaces. Anal. PDE, 2018. [arXiv] [Journal] [Thesis, Chapter 3]
See my profile on Google Scholar.
Lecture notes
Lecture notes
Lecture notes on instability and non-uniqueness in the Navier-Stokes equations. From my 4 hour minicourse at the UMN Summer Workshop on Analysis of PDEs. [Dropbox]
Instability and nonuniqueness for the 2d Euler equations in vorticity form, after M. Vishik (with E. Brué, M. Colombo, C. De Lellis, V. Giri, M. Janisch, and H. Kwon). Accepted to Annals of Mathematics Studies. [arXiv]
Thesis
Thesis
Regularity aspects of the Navier-Stokes equations in critical spaces, 2020. [pdf]
Content not published elsewhere: Chapter 2 contains a summary of the Navier-Stokes theory which is suitable for newcomers to the field. Chapter 3 contains a streamlined version of my 1st paper (Anal. PDE, 2018), though this version was not peer reviewed, and it is anyway superseded by my 1st paper with Barker (ARMA, 2019).
Press
Press
This work with E. Brué and M. Colombo was featured in Quanta, the Research Highlights of the NSF Mathematical Sciences Institutes, and in a Korean popular science magazine aimed at young people.
Split Rock Lighthouse, Minnesota
Teaching
Teaching
University of Wisconsin-Madison
University of Wisconsin-Madison
Fall 2025: Topics in PDE
Spring 2025: MATH 519 Ordinary Differential Equations
Fall 2024: MATH 719 Partial Differential Equations I
Spring 2024: MATH 519 Ordinary Differential Equations
Fall 2023: MATH 221 Calculus I
Princeton University
Princeton University
Spring 2023: MAT202 Linear Algebra
Fall 2022: MAT201 Multivariable Calculus
My wife, Laurel Ohm, is an applied mathematician.
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