Research
I use techniques from harmonic and functional analysis to analyze partial differential equations, especially those arising in fluid mechanics.
Publications and Preprints
Non-decaying solutions to the 2D dissipative quasi-geostrophic equations, with David Ambrose, Ryan Aschoff, and James P. Kelliher, Submitted for publication.
Local existence for the 2D Euler equations in a critical Sobolev space, with Nicholas Harrison, Nonlinear Analysis, 2025.
Global existence for a nonlocal multi-species aggregation-diffusion equation, with Zachary Radke, Quarterly of Applied Mathematics, 2025.
Existence of solutions to fluid equations in Holder and uniformly local Sobolev spaces, with David Ambrose, Daniel Erickson, and James P. Kelliher, Journal of Differential Equations, 2023.
Uniqueness for active scalar equations in a Zygmund space, Asymptotic Analysis, 2022.
Well-posedness of the 2D Euler equations when velocity grows at infinity, with James P. Kelliher, Discrete and Continuous Dynamical Systems, Series A, 2019.
The aggregation equation with Newtonian potential : the vanishing viscosity limit, with Gung-Min Gie and James P. Kelliher, Journal of Mathematical Analysis and Applications, 2017.
Incompressible Euler equations and the effect of changes at a distance, with James P. Kelliher, Journal of Mathematical Fluid Mechanics, 2016.
Solutions to the 2D Euler equations with velocity unbounded at infinity, Journal of Mathematical Analysis and Applications, 2015.
The axisymmetric Euler equations with vorticity in borderline spaces of Besov type, Journal of Dynamics and Differential Equations, 2014.
Vanishing viscosity in the plane for nondecaying velocity and vorticity II, Pacific Journal of Mathematics, 2014.
On optimal estimates for the Laplace-Leray commutator in planar domains with corners, with Robert Pego, Proceedings of the American Mathematical Society, 2011.
A finite time result for vanishing viscosity in the plane with nondecaying vorticity, Communications in Mathematical Sciences, 2010.
Vanishing viscosity in the plane for nondecaying velocity and vorticity, SIAM Journal on Mathematical Analysis, 2009.
An initial value problem for two-dimensional ideal incompressible fluids with continuous vorticity, Mathematical Research Letters, 2007.
Vanishing viscosity in the plane with vorticity in borderline spaces of Besov type, with James P. Kelliher, Journal of Differential Equations, 2007.