Academic Background
My research is focused on the analysis of partial differential equations. I received my PhD from New York University in 2014, where I was supervised by Professors Nader Masmoudi and Fang-Hua Lin. From 2014-2017 I was an instructor at Princeton University and from 2017-2020 I was an assistant professor at UC-San Diego. Since 2020, I've been at Duke. More information can be found in my CV.
Some Recent Preprints
A Classification Theorem for Steady Euler Flows, Y. Huang, A. Said, and C. Xie
Finite-time Singularity Formation for Scalar Stretching Equations, with R. Bianchini
Wellposedness and singularity formation beyond the Yudovich class, with R. Murray and A. Said
From Instability to Singularity Formation in Incompressible Fluids, with F. Pasqualotto
Norm Growth, Non-uniqueness, and Anomalous Dissipation in Passive Scalars, with K. Liss
Twisting in Hamiltonian flows and Ideal Fluids, with T. Drivas and I. Jeong
Optimal Enhanced Dissipation and Mixing for a time-periodic Lipschitz velocity field on $\mathbb{T}^2$, with K. Liss and J. Mattingly
On the long-time behavior of scale-invariant solutions to the 2d Euler equation and applications, with R. Murray and A. Said
Singularity Formation
Invertibility of a Linearized Boussinesq Flow: a Symbolic Approach, with F. Pasqualotto
Singularity formation in the Euler equation in finite and infinite time, with T. Drivas
The incompressible Euler equations under octahedral symmetry: singularity formation in a fundamental domain, with I. Jeong
Stable self-similar blowup for solutions to the incompressible Euler equation, with T. Ghoul and N. Masmoudi
Finite-time singularity formation for an active scalar equation, with S. Ibrahim and S. Shen
Stable self-similar blowup for a family of nonlocal transport equations, with T. Ghoul and N. Masmoudi
Finite-time singularity formation for strong solutions to the axi-symmetric $3D$ Euler equations, with I. Jeong
Finite-time singularity formation for strong solutions to the Boussinesq system, with I. Jeong
On the Effects of Advection and Vortex Stretching, with I. Jeong
Steady States & Long-time Behavior
Remark on the Stability of Energy Maximizers for the 2D Euler Equation on $\mathbb{T}^2$
Smooth and singular steady states to the 2d Euler equation on $\mathbb{T}^2$, with Y. Huang.
Stationary Structures near the Kolmogorov and Poiseuille Flows in the 2d Euler Equations, with M. Coti-Zelati and K. Widmayer
On 2d incompressible Euler equations with partial damping, with W. Hu and V. Sverak
Long-time stability for solutions of a Beta-plane Equation, with Klaus Widmayer
Sharp decay estimates for an anisotropic linear semigroup and applications to the SQG and inviscid Boussinesq systems, with K. Widmayer
Well-posedness Issues & Singularity Propagation
Strong ill-posedness for bounded solutions to the Riesz transform problem, with K. Shikh Khalil
Propagation of singularities by Osgood vector fields and for 2D inviscid incompressible fluids, with T. Drivas and J. La
On Singular Vortex Patches, I, with I. Jeong
On Singular Vortex Patches, II, with I. Jeong
$L^\infty$ ill-posedness for a class of equations arising in hydrodynamics, with N. Masmoudi
Symmetries and Critical Phenomena in Incompressible Fluids, with I. Jeong
Ill-posedness for the incompressible Euler equations in critical Sobolev spaces, with I. Jeong
Sharp $L^p$ estimates for singular transport equations
Osgood's lemma and results on the slightly supercritical 2-D Euler equations for incompressible flow
Mixing and Diffusion
Growth of Sobolev norms and loss of regularity in transport equations, with G. Crippa, A. Mazzucato, and G. Iyer
Anomalous Dissipation in Passive Scalar Transport, with T. Drivas, G. Iyer, and I. Jeong
Enhanced dissipation in the Navier-Stokes equations near the Poiseuille flow, with M. Coti-Zelati and K. Widmayer
On the relation between enhanced dissipation time-scales and mixing rates, with M. Coti-Zelati and M.G. Delgadino
Universal mixers in all dimensions, with A. Zlatos
Inviscid Limit and Complex Fluids
Inviscid limit of vorticity distributions for Yudovich solutions, with P. Constantin and T. Drivas
On Singularity formation in a Hele-Shaw model, with P. Constantin, H. Nguyen, and V. Vicol
The inviscid limit for the free surface Navier-Stokes equations with surface tension, with D. Lee
Global Regularity for Some Oldroyd-B Type Models, with F. Rousset
Remarks on the inviscid limit for the Navier-Stokes equations for uniformly bounded velocity fields, with P. Constantin, M. Ignatova, and V. Vicol
On some electroconvection models, with P. Constantin, M. Ignatova, and V. Vicol
On the inviscid limit of the 2D Navier-Stokes equations with vorticity belonging to BMO-type spaces, with F. Bernicot and S. Keraani
Homotopy method for the eigenvalues of symmetric tridiagonal matrices, with Philip Brockman, Timothy Carson, Yun Cheng, Mohamed Elgindi, Kristen Jensen, X Zhoun